Christopher K. R. T. Jones
Department of Mathematics
University of North Carolina-Chapel Hill
Chapel Hill, NC 27599-3250
1. Personal Information
2. Education
3. Employment
4. Visiting Appointments
5. Honours and Awards
6 Editorial Boards
7 Professional Service
8 Conference Organizing
9 Society Memberships
10 Grant Support ( 2000-present)
11 Short Courses
12 Other Presentations and Events ( 1998-present)
13 Lectures and Presentations ( 2000 present)
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
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)
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
Amal El Mograbhy, May 2004
Nicholas Constanzino, May 2005
Date of Completion: April 2, 2003