Christopher K. R. T. Jones
Department of Mathematics
University of North Carolina-Chapel Hill
Chapel Hill, NC 27599-3250

1. Personal Information

  • Born September 10, 1951
  • Citizen of United Kingdom
  • Permanent Resident of U. S.

    2. Education

  • University of Bristol, B. A. ( First Class) June 1974: Mathematics and Philosophy
  • University of New Mexico, Albuquerque, M. S. , May 1976: Mathematics
  • University of Wisconsin-Madison, Ph. D. Dec 1979: Mathematics ( Advisor: C. Conley)

    3. Employment

  • University of North Carolina at Chapel Hill: Guthridge Distinguished Professor of Mathematics, 2002-present
  • Brown University: Professor, 1990-2003 Director of the Lefschetz Center for Dynamical Systems, 1999-2002
  • University of Maryland-College Park: Associate Professor 1987 -1990
  • University of Maryland-College Park: Assistant Professor 1985-1987
  • University of Arizona: Assistant Professor 1981 -1985
  • University of Minnesota-Minneapolis: Visiting Assistant Professor 1980 -1981
  • University of British Columbia: Postdoctoral Fellow 1980 ( Jan -Jul)

    4. Visiting Appointments

  • University of Stuttgart: Visiting Research Professor, 1993-4
  • Woods Hole Oceanographic Institution: Guest Investigator, 2000-1

    5. Honours and Awards

  • Graduate Research Board Award, University of Maryland, 1989
  • Humboldt Award for Senior U. S. Scientist, 1993-1994
  • CNR Visting Professor and CIME Lecturer, Italy, June 1994
  • Plenary Lecturer, SIAM Conference on Applications of Dynamical Systems, Snowbird, 1997
  • Faculty Mentor of the Year Award, 1999, Compact for Faculty Diversity


    6 Editorial Boards

  • Coordinating Editor: Physica D
  • Dynamics and Differential Equations
  • Methods and Applications of Analysis
  • SIAM Journal of Dynamical Systems

    7 Professional Service

  • Chair: SIAM Activity Group on Dynamical Systems planning committee
  • Chair: Math Awareness Month Committee, 2001
  • Scienti c Advisory Committee: O ce of Naval Research DRI on Predictability, 2000-3
  • SIAM Representative to the American Association for the Advancement of Science, Section A, 2002-5
  • Chair, J. D. Crawford Prize Committee, SIAG on Dynamical Systems, SIAM, 2000-1
  • Committee on Mathematics in the Geosciences, 2001
  • Nominating Committee, SIAG on Dynamical Systems, SIAM, 2001
  • Board of Trustees, SIAM, 1998-2000
  • Chair: SIAM Activity Group on Dynamical Systems, 1993-5
  • SIAM Outstanding Paper Prize Committee, 2000
  • SIAM Conference Strategic Planning Task Force, 2000
  • Advisory Board: SIAM Activity Group on Dynamical Systems, 1995-7

    8 Conference Organizing

  • Co-organizer: SIAM Meeting on Applications of Dynamical Systems, Snowbird, Utah, October 1992
  • Organizer: ONR Workshop on Dynamical Systems and Oceanography, Little Compton, RI, May 1993
  • Organizing Committee: SIAM Annual Meeting, Kansas City, July 1996
  • Co-organizer: Workshop on Dynamical Systems and Nonlinear Optics May, 1997, Rhode Island
  • Chair of organizing committee: Workshop on Multiple Time Scale Dynamical Systems Oct. 1997, IMA, Minnesota.
  • Organizer: Workshop on Dynamical Systems Methods for Lagrangian Transport in the Ocean May, 1998, IMA, Minnesota.
  • Co-organizer: Workshop on Recent Advances in the Stability Theory of Nonlinear Waves May, 1998, Rhode Island.
  • Member of Scienti c Committee for Paci c-Rim Dynamical Systems Conference, Hawaii, August, 2000.
  • Member of Program Committee for Conference in honour of 100th anniversary of birth of A. A. Andronov, Nizhny Novgorod, July, 2001
  • Co-organizer: Mininsymposium on Dynamics of Nonlinear Waves at rst French-American Math-ematical Congress, Lyon, July 2001
  • Co-organizer: Minisymposium on Transport across scales in the ocean and atmosphere SIAM 50th Anniversary Meeting, Philadelphia, PA, July 2002
  • Co-organizer: Mini-workshop at Oberwolfach on Dynamics of nonlinear waves January, 2003

    9 Society Memberships

  • American Mathematical Society
  • Society of Industrial and Applied Mathematics
  • Optical Society of America
  • American Geophysical Union
  • American Association for the Advancement of Science.

    10 Grant Support ( 2000-present)

  • National Science Foundation 1997-2001 International exchange grant with Germany on Dynamical Systems Techniques in Nonlinear Optics
  • Office of Naval Research 1998-2000 Expansion grant for collaborative research on predictability with Woods Hole Oceanographic In-
    stitution and the College for Marine Studies at the University of Delaware.
  • National Science Foundation, 2000-2003 FRG grant for Collaborative Research on High Bit-Rate Communication: From Mathematical
    Development to Fiber Design
  • Office of Naval Research 2000-2005 Uncovering the Geometry of Ocean Flows: Implications for Predictability and Experimental
    Design
  • National Science Foundation, 2002-2004 University-Industry Cooperative Grant with Corning Inc. Pulse Dynamics in Optical Communi-
    cations

    11 Short Courses

  • Lectures on Geometric Singular Perturbation Theory CIME, Montecatini-Terme, June 1994
  • Lecture Series on Singular Perturbation Theory College of Enginnering, University of Illinois, March 1996
  • Summer School on Nonlinear Oscillations, Waves and Patterns , Cork, Ireland, Summer 1996, 1997
  • Tutorial lectures at Workshop on Dynamical Systems and Oceanography, Woods Hole, MA, De-cember 1996
  • Lecture Series on Singular Perturbation Theory University of California at Santa Barbara, College of Engineering, April 1997
  • Tutorial on Multiple Time Scales in Dynamical Systems IMA, Minnesota, October 1997
  • Summer School Optical Pulse Propagation Twente, Holland, June 2002

    12 Other Presentations and Events ( 1998-present)

  • Presentation to National Research Council Committee on Interdisciplinary Research involving Mathematics, National Academy of Sciences, Washington, DC, March 1998
  • Poster presentation as part of Research in the National Defense representing the Joint Policy Board on Mathematics, US Congress, April 1998
  • Presentation on The Pros and Cons of Postdoctoral Appointments at the Compact for Faculty Diversity Annual Institute, Orlando, FL, October 2000
  • Interview on Pat Kenschaft s Math Medley hour long radio show broadcast April 21, 2001
  • Presentations on The Road to Tenure and Security a Postdoc and Managing your Superviser at the Compact for Faculty Diversity Annual Institute, Atlanta, GA, October 2001
  • Presentations on The Postdoctoral Experience and Networking for Early Career Development at the Compact for Faculty Diversity Annual Institute, Arlington, VA, October 2002
  • Invited particpant: Approaches to Combat Terrorism organized by NSF and the Intelligence Community, Chantilly, VA, November 2002

    13 Lectures and Presentations ( 2000 present)

  • Invited lecture, Dynamics Days 2000, Santa F ´ e, January 2000
  • European Geophysical Society, lecture in session on Mixing and Transport, Nice, France, April 2000
  • ONR Workshop on Predictability, Nice, France, May 2000
  • Minisymposium lecture, SIAM Annual Meeting, Puerto Rico, July 2000
  • Colloquium, University of Pittsburgh, October 2000
  • Colloquium, Harvard University, November 2000
  • Colloquium, University of Missouri, November 2000
  • Invited Talk, Show-Me Seminar , Rolla, Missouri, November 2000
  • Physical Oceanography Seminar, Woods Hole Oceanographic Institution, December 2000
  • American Geophysical Union Annual Meeting, San Francisco, December 2000
  • Lecture, University of Cologne, January 2001
  • Invited lecture, Conference on Statistical and Nonlinear Physics of Fiber Communications, Los Alamos, March 2001
  • Applied Mathematics Colloquium, Simon Fraser University, Vancouver, BC, March 2001
  • Colloquium, Indiana University, Bloomington, April 2001
  • PACM Colloquium, Princeton University, April 2001
  • Lecture for Mathematics Awareness Month, Raytheon Corporation, Portsmouth RI, April 2001
  • Minisymposium lectures, SIAM Conference on Applications of Dynamical Systems, Snowbird, May 2001
  • Contributed Lecture ( Union Session) , American Geophysical Union spring meeting, May 2001
  • Conference on Nonlinear Phenomena in Science, Amsterdam, June 2001
  • Conference on Nonlinear Dynamics and Chaos: Where do we go from here? Bristol, UK, June 2001
  • Seminar, University of Warwick, UK, June 2001
  • Lecture, GFD Summer Program, Woods Hole Oceanographic Institution, August, 2001
  • CAMP Seminar, University of Chicago, October, 2001
  • Invited lecture, Midwest Dynamical Systems Seminar, Boulder, CO, October, 2001
  • Colloquium, Morehouse College, Atlanta, GA, October 2001
  • Plenary lecture, Applied Mathfest, University of Arizona, November 2001
  • Seminar, University of Wisconsin-Madison, November 2001
  • NSC One day workshop, Hokkaido, Japan, November 2001
  • Plenary Speaker, Frontiers of Applied Analysis, 60th birthday celebration of Mimura nd Nishida, Fukuoka, Japan, December, 2001
  • Conference on Nonlinear Analysis, Kloster-Irsee, Germany, January 2002
  • Applied Mathematics Seminar, University of North Carolina-Chapel Hill, January 2002
  • Control and Dynamical Systems Seminar, Mechanical Engineering, University of California at Santa Barbara, February 2002
  • Applied Mathematics Seminar, University of California at Santa Barbara, February 2002
  • Colloquium, University of Virginia, March 2002
  • Colloquium, University of Massachusetts-Amherst, April 2002
  • Main lecture, Applied Math Days, RPI, April 2002
  • Colloquium, Engineering Sciences and Applied Mathematics, Northwestern University, April 2002
  • Workshop on Data Assimilation in the Ocean and Atmosphere IMA, Minnesota, May 2002
  • ONR Workshop on Predictability in the Ocean and Atmosphere CDC, Boulder, Colorado, May 2002
  • Office of Naval Research Invited Lecture, Arlington, VA, July 2002
  • Minisymposium on Optical Communications at SIAM Annual Meeting, Philadelphia, July 2002
  • Invited talk at Optical Society of America Annual Meeting, Orlando, October, 2002
  • Seminar, North Carolina State University, November, 2002
  • LAPCOD 2002, Key Largo, Florida, December 2003
  • Minisymposium on Dynamical Systems and Oceanography at the AMS Annual Meeting, Balti-more, January, 2003
  • Workshop on Raman-Based High-Speed Photonics Los Alamos National Labs, February 2003
  • Seminar in Atmospheric Sciences, UCLA, February 2003
  • Workshop on Emerging Applications of the Nonlinear Schr ¨ odinger Equation IPAM, UCLA, Febru-ary 2003
  • Applied Mathematics Seminar, Duke University, February 2003
  • Workshop on Physical-Statistical Modelling and Data Assimilation SAMSI, Durham, March 2003
  • Minisymposium lecture, IMACS Conference on Nonlinear Waves, Athens, GA, April 2003
  • Conference on Dynamical Systems and Neuroscience, 60th birthday of Nancy Kopell, Boston, MA, April 2003
  • Minisymposium lectures, SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 2003

    14 Publications in Refereed Journals
    1. Spherically symmetric solutions of a reaction-diffusion equation Journal of Differential Equations, 49 ( 1983) 142-169

    2. Asymptotic behavior of a reaction-diffusion equation in higher space dimensions Rocky Mountain Journal of Math, 13 ( 1983) 355-364

    3. The -calculus Zeitschr. f. math. Logik und Grundlagen d. Math. 97 ( 1981) 97-110 ( with P. Kelemen)

    4. Characterization of bifurcation from the continuous spectrum by nodal properties Journal of Differential Equations, 45 ( 1984) 196-220 ( with T. K ¨ upper)

    5. Stability of the travelling wave solution of the FitzHugh-Nagumo system Transactions of the American Mathematical Society, 286 ( 1984) 431-469

    6. On the in nitely many solutions of a semilinear elliptic equation SIAM Journal of Math Analysis, 17 ( 1986) 803-835 ( with T. K ¨ upper)

    7. Chaos and coherent structures in partial differential equations Proceedings of the Symposium on Coherent Structures, Physica D, 18 ( 1986) 85-112 ( with A. Aceves et al. )

    8. Instability of standing waves in nonlinear optical waveguides Physics Letters A, 117 ( 1986) 175-180 ( withJ. Moloney)

    9. Instability of standing waves for nonlinear Schr ¨ odinger type equations Ergodic Theory and Dy-namical Systems, 8 ( 1988) 119-138

    10. An instability mechanism for radially symmetric standing waves of nonlinear Schr ¨ odinger equa-tions Journal of Differential Equations, 17 ( 1988) 34-62

    11. A shooting argument with oscillation for semilinear elliptic radially symmetric equations Pro-ceedings of the Royal Society of Edinburgh, 108A ( 1988) 165-180 ( with T. K ¨ upper and H. Plakties)

    12. Radial solutions of a semilinear elliptic equation at the critical exponent Archive for Rational Mechanics and Analysis, 104 ( 1988) 251-270

    13. Jumping stable manifolds for dissipative maps of the plane Physica D, 35 ( 1988) 87-106 ( with S. Hammel)

    14. Invariant manifolds for semilinear partial differential equations Dynamics Reported, 2 ( 1989) 1-38 ( with P. Bates)

    15. Travelling waves of a perturbed diffusion equation arising in a phase field model Indiana University Journal of Mathematics, 30 ( 1989) 1198-1222 ( with R. Gardner)

    16. A topological invariant arising in the stability analysis of travelling waves Journal f ¨ ur die reine und angewandte Mathematik, 410 ( 1990) 167-212 ( with J. Alexander and R. Gardner)

    17. Nearly real fronts in a Ginsburg Landau equation Proceedings of the Royal Society of Edinburgh, 116A ( 1990) 193-206 ( with T. Kapitula and J. Powell)

    18. A stability index for steady state solutions of boundary value problems for parabolic systems Journal of Differential Equations, 91 ( 1991) 181-203 ( with R. Gardner)

    19. Stability of travelling wave solutions of diffusive predator prey systems Transactions of the Amer-ican Mathematical Society, 377 ( 1991) 465-524 ( with R. Gardner)

    20. Competition between generic and non-generic fronts in envelope equations Physical Review A, 44 ( 1991) 3636-3652 ( with J. Powell and A. Newell)

    21. Tracking invariant manifolds with differential forms in singularly perturbed systems Journal of Differential Equations, 108 ( 1994) 64-88 ( with N. Kopell)

    22. A geometric proof of the Kwong McLeod uniqueness result SIAM Journal of Math Analysis, 24 ( 1993) 436-443 ( with C. Clemons)

    23. Existence and stability of asymptotically oscillatory double pulses, Journal f ¨ ur die reine und angewandte Mathematik, 446 ( 1994) 49-79 ( with J. Alexander)

    24. Stability of travelling waves in non-convex scalar viscous conservation laws Communications in Pure and Applied Math, 46 ( 1993) 505-526 ( with R. Gardner and T. Kapitula)

    25. Existence and stability of asymptotically oscillatory triple pulses ZAMP, 44 ( 1993) 189-200 ( with J. Alexander)

    26. Instability of quasiperiodic solutions of the Ginsburg -Landau equations Proceedings of the Royal Society of Edinburgh, 125A ( 1995) 501-517 ( with A. Doelman and R. Gardner)

    27. A mechanism for capture into resonance Physica D, 69 ( 1993) 85-106 ( with T. Burns)

    28. Tracking invariant manifolds up to exponentially small errors SIAM Journal of Math Analysis, 27 ( 1996) 558-577 ( with T. Kaper and N. Kopell)

    29. Invariant Manifolds and Singularly Perturbed Boundary Value Problems SIAM Journal of Nu-merical Analysis, 31 ( 1994) 1558-1576 ( with S. -K. Tin and N. Kopell)

    30. Stability of the in-phase travelling wave solution in a pair of coupld nerve bers Indiana University Journal of Math, 44 ( 1995) 189-220 ( with A. Bose)

    31. Settling and asymptotic motion of aerosol particles in a cellular flow field J. Nonlinear Science, 5 ( 1995) 337-358 ( with M. Maxey and J. Rubin)

    32. The existence of travelling wave solutions of a generalized phase- field model SIAM Journal of Math Analysis, 28 ( 1997) 60-93 ( with P. Bates, P. Fife and R. Gardner)

    33. Stability of pulses on optical bers with phase-sensitive ampli ers ZAMP, 48 ( 1997) 175-192 ( with J. Alexander, M. Grillakis, B. Sandstede)

    34. Existence and stability of N -pulses on optical bers with phase-sensitive ampli ers Physica D, 106 ( 1997) 167-206 ( with B. Sandstede and J. Alexander)

    35. Phase field models for hypercooled solidi cation Physica D, 104 ( 1997) 1-31 ( with P. Bates, P. Fife and R. Gardner)

    36. Quantifying transport in numerically generated velocity fields Physica D, 110 ( 1997) 105-122 ( with P. Miller, A. Rogerson and L. Pratt)

    37. Existence of standing pulse solutions to an inhomogeneous reaction-diffusion equation Journal of Dynamics and Differential Equations, 10 ( 1998) 1-35 ( with J. Rubin)

    38. Bifurcations and edge oscillations in the semiconductor Fabry-P ´ erot interferometer Optics Com-munications, 140 ( 1997) 93-98 ( with J. Rubin)

    39. Viscous perturbations of vorticity conserving flows and splitting of separatrices Nonlinearity, 11 ( 1998) 47-77( with B. Sandstede and S. Balasuriya)

    40. The existence of travelling wave solutions of a generalized phase field model SIAM Journal of Math Analysis, 28 ( 1997) 60-93 ( with P. Bates, P. Fife and R. Gardner)

    41. Average dynamics of the optical soliton in communication lines with dispersion management: analytical results Phys Rev E, 58 ( 1998) 48-51 ( with A. Aceves, S. Turitsyn and V. Zharnitsky)

    42. Hamiltionian averaging in soliton-bearing systems with a periodically varying dispersion Phys Rev E, 59 ( 1999) 3843-3846 ( with S. Turitsyn, A. Aceves and V. Zharnitsky)

    43. Lagrangian motion and fluid exchange in a barotropic meandering jet Journal of Physical Oceanog-raphy, 29 ( 1999) 2635-2655 ( with A. Rogerson, P. Miller and L. Pratt)

    44. Bifurcation of internal solitary wave modes from the essential spectrum Phys Rev E, 61 ( 2000) 3114-3121 ( with P. Kevrekidis)

    45. Bifurcation of asymmetric solutions in nonlinear optical media ZAMP, 52 ( 2001) 859-880 ( with T. K ¨ upper and K. Scha ner)

    46. A spectral mapping theorem and invariant manifolds for nonlinear Schr ¨ odinger equations Indiana U. Math. Journal, 49 ( 2000) 221 243 ( with F. Geszetesy, Y. Latushkin and M. Stanislavova)

    47. Instability of multiple pulses in coupled nonlinear Schr ¨ odinger equations Phys Rev E, 61 ( 2000) 5886-5892 ( with A. C. Yew and B. Sandstede)

    48. Melnikov theory for nite-time vector fields Nonlinearity, 13 ( 2000) 1357-1377 ( with B. Sandstede, S. Balasuriya and P. Miller)

    49. Exponentially small splitting of heteroclinic orbits: from the rapidly forced pendulum to discrete solitons Physics Letters A, 269 ( 2000) 120-129 ( with P. Kevrekidis and T. Kapitula)

    50. Reconstructing basin-scale Eulerian velocity fields from simulated drifter data Journal of Physical Oceanography, 31 ( 2001) 1361-1376 ( with M. Toner, A. Poje. A. D. Kirwan Jr. , B. Lipphardt and C. Grosch)

    51. Stabilizing e ects of dispersion management Physica D 152-3 ( 2001) 794-817 ( with V. Zharnitsky, E. Grenier and S. Turitsyn)

    52. Ground states of dispersion manged NLS Phys Rev E 62 ( 2000) 7358 ( with V. Zharnitsky, E. Grenier, J. Hesthaven and S. Turitsyn)

    53. Stability of neuronal pulses composed of two concatenated unstable kinks Phys Rev E 63 ( 2001) 011904-1 ( with M. Romeo)

    54. Soliton internal modes: pure power law? Phys Rev E, 63 ( 2001) 036602 ( with P. Kevrekidis and T. Kapitula)

    55. diffusive draining and growth of eddies Nonlinear Processes in Geophysics, 8 ( 2001) 241-251 ( with S. Balasuriya)

    56. Chaotic transport of mass and potential vorticity for an island recirculation Journal of Physical Oceanography, 32 ( 2002) 80-102 ( with P. Miller, L. Pratt and K. Helfrich)

    57. Barrier Destruction and Lagrangian predictability at depth in a meandering jet Dynamics of Atmospheres and Oceans, 35 ( 2002) 41-61 ( with G. Yuan and L. Pratt)

    58. Stability of multiple pulses in noisy optical bers with phase-sensitive ampli cation Optical Com-munications, 195 ( 2001) 127-139 ( with R. Moore, B. Sandstede, W. Kath and J. Alexander)

    59. Drifter launch strategies based on dynamic Lagrangian templates Journal of Physical Oceanog-raphy, 32 ( 2002) 1855-1869 ( with A. Poje, M. Toner and A. D. Kirwan Jr. )

    60. The Loop Current and adjacent rings delineated by Lagrangian analysis in near surface flows Jour-nal of Marine Research, 60 ( 2002) 405-429 ( with L. Kuznetsov, M. Toner, A. D. Kirwan Jr. , L. Kantha

    and J. Choi)
    61. Dispersion managed solitons via an averaged variational principle to appear in Physica D ( with R. Jackson and V. Zharnitsky)

    62. Pulse propagation in media with deterministic and random dispersion variations Optics Commu-nications, 214 ( 2002) 353 -362 ( with T. Sch ¨ afer and R. Moore)

    63. Pulse stabilization by high order dispersion management to appear in Optics Letters ( with J. Moeser and I. Gabitov)

    64. Weak Melnikov theory and 3-D viscous flows to appear in Physica D ( with S. Balasuriya and I. Mezi ´ c)

    65. Chloropohyll dispersal by eddy-eddy interactions in the Gulf of Mexico to appear in Journal of Geophysical Research ( with M. Toner, A. D. Kirwan, L. Kantha and F. Muller-Kr ¨ ager)

    66. Lagrangian data assimilation for point vortex systems Journal of Turbulence, 3 ( 2002) 1-7

    67. The stability of travelling calcium pulses in a pancreatic acinar cell Physica D, 177 ( 2003) 242-258 ( with M. Romeo)

    68. On strati ed shear flow in sea straits of arbitrary cross-scetion to appear in Studies in Applied Math ( with J. Deng, L. Pratt and L. Howard)

    69. Assessing coherent feature kinematics in ocean models to appear in Physica D ( with L. Kuznetsov, M. Toner and A. D. Kirwan Jr. )

    70. A method for assimilation of Lagrangian data to appear in Monthly Weather Review ( with K. Ide and L. Kuznetsov)


    15 Papers in Conference Proceedings and Other Collections
    1. Some ideas in the proof that the FitzHugh-Nagumo pulse is stable in Nonlinear Partial Differential Equations, J. Smoller ed. , Contemporary Mathematics 17, AMS, 1984

    2. A mechanism for chaos in a nonlinear optical system in Optical Bistability II, C. Bowden, H. Gibbs and S. McCall eds. , Plenum Press, 1984 ( with S. Hammel and J. Moloney)

    3. Invariant manifolds with applications in Nonlinear Functional Analysis and its Applications, S. P. Synge ed. , Nato Advanced Studies Institute, D. Reidel, Amsterdam, 1986 ( with P. Bates)

    4. On the in nitely many standing waves of some nonlinear Schr ¨ odinger equations in Nonlinear Systems of Partial Differential Equations in Applied Mathematics Part II, B. Nicolaenko, D. Holm

    and J. Hyman eds. , Lectures in Applied Mathematics 23, AMS, 1986

    5. Stability and instability of nonlinear standing waves in planar optical waveguides in Opt. Bistab. III, H. Gibbs, P. Mandel, N. Peyghambarian and S. D. Smith eds. , Springer Proc. in Physics 8, 1986 ( with J. Moloney)

    6. Standing Waves of nonlinear Schr ¨ odinger equations: existence and stability in Material Instabil-ities in Continuum Mechanics and Related Mathematical Problems, J. M. Ball ed. , Oxford, 1988

    7. The solutions of the nonlinear Klein Gordon equation near a steady state in Advanced Topics in the Theory of Dynamical Systems, G. Fusco, N. Ianelli and L. Salvadore eds. , Academic Press, 1989

    ( with P. Bates)

    8. Construction of the FitzHugh Nagumo pulse using differential forms , in Patterns and Dynamics in Reactive Media, R. Aris, D. Aronson and H. Swinney eds. , IMA vol. 37, Springer-Verlag, NY, 1991 ( with N. Kopell and R. Langer)

    9. Stability of one-dimensional waves in weak and singular limits , in Viscous Pro les and Numerical Methods for Shock Waves, M. Shearer ed. , SIAM Proceedings in Applied Mathematics 56, 1991 ( with R. Gardner)

    10. On the significance of homoclinic orbits to chaotic motion in The Chaos Paradigm: Develop-ments and Applications in Engineering and Science, R. Katz ed. , Proceedings of the ONR/ NUWC Conference, Mystic, CT, April 1993, AIP Conference Proceedings 296

    11. Chaotic mixing across oceanic jets Proc. ONR/ NUWC Conference on Nonlinear Signal Process-ing, Mystic, CT, July 1995 ( with P. Miller, G. Haller and L. Pratt)

    12. Stable multiple pulses in optical bers with phase-sensitive ampli cation Proceedings of the Optical Society of America meeting: Nonlinear Guided Waves and their Applications, 1998 ( with R. Moore, W. Kath, J. Alexander and B. Sandstede)

    13. A primer on the Exchange Lemma in fast-slow systems to appear in Multiple Time Scale Dy-namical Systems, IMA Proceedings, Springer-Verlag, 2000 ( with T. Kaper)

    14. Invariant Manifolds and Lagrangian Dynamics in the Ocean and Atmosphere Handbook of Dy-namical Systems: Towards Applications, B. Fiedler ed. , Elsevier, 2002 ( with S. Winkler)

    15. Random dispersion on bers carrying optical pulses , NLGW, Stresa, Italy, September, 2002 ( with T. Sch ¨ afer and R. Moore)

    16. A Scheme for the assimilation of Lagrangian data Proceedings of Fluid Dynamics conference, Santa Barbara, CA, March, 2002 ( with K. Ide and L. Kuznetsov)

    16 Papers Submitted
    1. A symplectic view of a semilinear elliptic boundary value problem submitted to AMS Electronic Research Announcements ( With J. Deng)

    2. Relative dispersion, transport barriers and chaotic advection in the Antarctic polar vortex sub-miited to Dynamics of Atmospheres and Oceans ( with S. Winkler)

    3. Estimating the predictability of an oceanic time series using Linear and nonlinear methods ( with G. Yuan, S. Lozier and L. Pratt)

    4. Cross-jet transport and mixing in a 2 1 2 layer ( with G. Yuan and L. Pratt)

    5. Pulse propagation in the presence of third order dispersion management submitted to SIAM J Applied Math ( with J. Moeser, I. Gabitov and V. Zharnitsky)

    17 Papers in Preparation
    1. Generalized exchange lemmas and orbits heteroclinic to invariant manifold ( with S. -K. Tin)

    2. Cross jet transport and mixing in a 2 1 2 layer model ( with G. Yuan and L. Pratt)

    3. Stable pulse solutions for the nonlinear Schr ¨ odinger equation with higher order dispersion man-agement ( with J. Moeser, I. Gabitov and V. Zharnitsky)

    18 Lecture Notes
    1. Geometric Singular Perturbation Theory C. I. M. E. Lectures, Montecatini Terme, June 1994, Lec-ture Notes in Mathematics 1609, Springer-Verlag, Heidelberg, 1995.

    19 Edited Volumes
    1. Dynamics Reported ( New Series) Expositions in Dynamical Systems, Volumes I-IV, Springer-Verlag 1991-5 ( with H. -O. Walther and U. Kirchgraber)

    2. Multiple Time Scale Dynamical Systems, IMA Proceedings vol. 122, Springer-Verlag, NY, 2000 ( with A. Khibnik)

    20 Other Publications
    1. Dynamical Systems at ICIAM 1991, SIAM News, October, 1991

    2. Settling and chaotic mixing in oceanic flows: the r ole of heteroclinic orbits , Naval Research Reviews, O ce of Naval research, 46 ( 1995) 17-28 ( with G. Haller, P. D. Miller and J. Rubin) .

    3. A geometric approach to systems with multiple time scales Journal of the Japanese SIAM, 7 ( 1997) 39-48 ( in Japanese-translated by K. Sakamoto)

    4. A Dynamics Group Looks at the Ocean SIAM News, March, 2000

    5. Whither Applied Nonlinear Dynamics Mathematics Unlimited: 2001 and Beyond, Vol. II, Springer-Verlag

    6. Lagrangian Predictability in Ocean Flows in ONR report based on DRI Workshop, Nice, May 2000

    7. A Rational Approach to Earth Management SIAM News July/ August 2001


    21 Students and Postdocs

  • Postdoctoral Fellows mentored:

    Tasso Kaper ( 1991-2) ; curent position: Assoc. Prof. , Boston U. ( Sloan Fellow and NSF Young
    Investigator)
    Pat Miller ( 1994-7) ; current position: Assoc. Prof. , Stevens Inst. Tech.
    Bjoern Sandstede ( 1995-6) ; current position: Assoc. Prof. , Ohio State U. ( Sloan Fellow and JD Crawford Prize winner)
    Andrew Poje ( 1996-9) ; current position: Asst. Prof. , CUNY-Staten Island
    Vadim Zharnitsky ( 1997-2000) ; current position: Researcher, Bell Labs.
    Sanjeeva Balasuriya ( 1999-2000) ; current position: Lecturer in Applied Mathematics, University of Sydney, Australia
    Shunsaku Nii ( 1997-8) ; current position: Asst. Prof. , Saitama U.
    Peter Howard ( 1998-9) ; current position: Asst. Prof. , Texas A& M
    Leonid Kuznetsov ( 1999-present) ;
    Guocheng Yuan ( 1999-2002, jointly mentored with Larry Pratt at Woods Hole Oceanographic Institution and Susan Lozier, Geosciences, Duke University) ; current position: Researcher, NCEP
    Tobias Schaefer ( 2001-present) ;
    Richard Moore ( 2001-2002)
    Rudy Horne ( 2002-present)
    Jie Yu ( 2003-present)

  • Ph. D. Theses directed:

    Steven Hammel, 1985
    -- Thesis: A dissipative map of the plane-a model for optical bistability
    -- Current position: Reseach Scientist, Space and Sea Systems Labs, US Navy, San Diego

    Curtis Clemons, 1990
    -- Thesis: Uniqueness results for semilinear elliptic equations
    -- Current position: Assoc. Prof. , University of Akron

    Todd Kapitula, 1991
    -- Thesis: Stability of travelling waves with applications to Ginsburg-Landau equations
    -- Current position: Assoc. Prof. , Univ. New Mexico

    Amit Bose, 1993
    -- Thesis: Dynamics of coupled nerve bers
    -- Current position: Assoc. Prof. , New Jersey Inst. Tech.

    Siu-Kei Tin, 1994
    -- Thesis: On the dynamics of tangent spaces near a normally hyperbolic manifold
    -- Stella Dafermos Award, 1994
    -- Current position: Researcher, Amiable Technologies.

    Jonathan Rubin, 1996
    -- Thesis: The generation of edge oscillations in an inhomogeneous reaction-diffusion equa-tion
    -- Current position: Asst. Prof. , Univ. Pittsburgh

    Sanjeeva Balasuriya, 1996
    -- Thesis: Viscosity induced transport in barotropic jets
    -- Dean's Fellow 1992; Stella Dafermos Award 1996
    -- Current position: Asst. Prof. Oberlin College

    Alice Yew 1998
    -- Thesis: An analytic study of solitary waves in quadratic media
    -- Dean s Fellow 1994-5; Ostrach Fellow 1996-7; Stella Dafermos Award 1998
    -- Current position: Asst. Prof. Ohio State U.

    Sean Winkler 2001
    -- Thesis: Lagrangian dynamics in geophysical fluid flows
    -- Sigma-Xi award, 2001
    -- Current position: Researcher, MIT Lincoln Labs.

    Monica Romeo 2001
    -- Thesis: Stability analysis of travelling pulses composed of concatenated kinks
    -- NSF Minority Fellow 1996-8; Ostrach Fellow 1999-2000; Stella Dafermos Award 2001
    -- Current position: VIGRE Postdoctoral Fellow, Duke University.

    Jamison Moeser 2002
    -- Thesis: Stable pulse propoagation in optical bers with varying dispersion
    -- Summer Intern, Los Alamos National Labs, Summer 2000, 2001
    -- Current position: VIGRE Postdoctoral Fellow, Applied Mathematics, University of Col-orado, 2002-4;

    Jian Deng 2002,
    -- Thesis: Instability of waves ane patterns in Hamiltonian systems and the Maslov index
    -- SIAM Student Paper Prize 2000,
    -- Sigma Xi award, 2002,
    -- Current position: von Karman Instructor, Applied Mathematics, Caltech, 2002-4;

    Russell Jackson, 2002
    -- Thesis: Multiple pulses in nonlinear optical systems
    -- Summer Intern, Lucent Technologies, Summer 2001
    -- Current position: NSF Postdoctoral Fellow, 2002-5 ( Boston U) .

    Jean-Michelet Jean-Michel, October 2002
    -- Thesis: Silnikov orbits in the equations for semiconductor lasers subject to optical injec-tion
    -- Instructor, University of Miami, 1998-9;
    -- Panel at Compact for Faculty Diversity Atlanta, 2001

  • Ph. D. Theses under direction ( with expected completion dates)

    Amal El Mograbhy, May 2004
    Nicholas Constanzino, May 2005

    Date of Completion: April 2, 2003