Publications in Refereed Journals
    2009
  1. "Existence of multi-pulse solutions of the regularized short pulse and Ostrovsky equations," accepted by JDDE. (with V.Manukian, N.Costanzino and B. Sandstede)
  2. "Solitary waves of the regularized short pulse and Ostrovsky equations," accepted by SIAM Journal of Mathematical Analysis (with N.Costanzino and V. Manukian)
  3. "Capturing deviation from ergodicity at different scales," accepted by Physica D (with S.Scott, T.C.Redd, L.Kuznetsov, and I.Mezic)
  4. "Multi-dimensional Morse index theorems and a symplectic view of elliptic boundary value problems," accepted by Transactions AMS (with J.Deng)
  5. "Generalized exchange lemmas and orbits heteroclinic to invariant manifolds," Discrete and Continuous Dynamical Systems 2 (2009) (with S.-K.Tin)
  6. "On the stability of high Lewis number combustion fronts," Discrete and Continuous Dynamical Systems 24 (2009) (with A.Ghazaryan)

    7. 2008
  7. "The suppression of four-wave mixing by random dispersion," to appear in SIAM Journal of Applied Mathematics 69 (2008) (with R.Horne and T. Schäfer)
  8. "Electrical waves in a one-dimensional model of cardiac tissue," SIAM Journal of Applied Dynamical Systems 7 (2008) 1558-1581 (with M.Beck, D.Schaefer and M.Wechselberger)
  9. "Data assimilation: mathematical and statistical perspectives," Int. J. Num. Meth. Fluids 56 (2008) 1033-1046 (with A.Apte, A.M.Stuart and J.Voss)
  10. "A Bayesian approach to Lagrangian data assimilation," Tellus A 60 (2008) 336-347 (with A.Apte and A.Stuart)
  11. "Modified particle filter methods for assimilating Lagrangian data into a point-vortex model," Physica D 237 (2008) 1498-1506 (with E.T. Spiller, A. Budhiraja, and K. Ide)
  12. "Using flow geometry for drifter deployment in Lagrangian data assimilation," Tellus A 60 (2008) 321-335 (with H.Salman and K.Ide)

    13. 2007
  13. "Solitary waves under the competition of linear and nonlinear periodic potentials," J.Phys.A 40 (2007) 14151-14163 (with Z.Rapti, P.Kevrekidis and V.Konotop)
  14. "Traveling waves in porous media combustion: uniqueness of waves for small thermal diffusivity," JDDE 19 (2007) 951-966 (with A.Ghazaryan and P.Gordon)

    15. 2006
  15. "A Method for Assimilating Lagrangian Data into a Shallow-Water Equation Ocean Model,” Monthly Weather Review 134 (2006) 1081-1101 (with H. Salman, L.Kuznetsov and K.Ide)

    16. 2005
  16. "Soliton broadening under random dispersion fluctuations: Importance sampling based on lowdimensional reductions" Optics Communications 259 (2005) 439-450 (with R.Moore and T.Schäfer)
  17. "The e¤ects of weak randomness on pulse interactions and four-wave mixing products" Physica D 205 (2005) 70-79 (with R.Horne and T. Schäfer)
  18. "“Ultra-short pulses in linear and nonlinear media", ”Nonlinearity 18 (2005) 1351-1374 (with.Y.Chung, E.Wayne and T.Schäfer)
  19. "Viscous perturbations of marginally stable Euler flow and finite-time Melnikov theory" Nonlinearity 18 (2005) 465-483(with B.Sandstede, F.Rousset and E.Grenier)
  20. "Ultra-short pulses in linear and nonlinear media," Nonlinearity 18 (2005) 1351-1374 (with.Y.Chung, E.Wayne and T.Schäfer)
  21. "The effects of weak randomness on pulse interactions and four-wave mixing products" Physica D 205 (2005) 70-79 (with R.Horne and T. Schäfer)
  22. "Soliton broadening under random dispersion fluctuations: Importance sampling based on low-dimensional reductions" to appear in Optics Communications (with R.Moore and T.Schäfer)
  23. "A Method for Assimilating Lagrangian Data into a Shallow-Water Equation Ocean Model," to appear in Monthly Weather Review (with H. Salman, L.Kuznetsov and K.Ide)

    24. 2004
  24. "Dispersion managed solitons via an averaged variational principle" Physica D 190 (2004) 63-77 (with R.Jackson and V.Zharnitsky)
  25. "Assessing coherent feature kinematics in ocean models" Physica D 191 (2004) 81-105 (with L.Kuznetsov, M.Toner and A.D.Kirwan Jr.)
  26. "Stable pulse solutions for the nonlinear Schrödinger equation with higher order dispersion management" SIAM J Applied Math 35 (2004) 1486-1511 (with J.Moeser and V.Zharnitsky)
  27. "Estimating the predictability of an oceanic time series using Linear and nonlinear methods" JGR-Oceans 109 (2004) (with G.Yuan, S.Lozier and L.Pratt)
  28. "Cross-jet Lagrangian transport and mixing in a 2½ layer" Journal of Physical Oceanography 34 (2004) 1991-2005 (with G.Yuan and L.Pratt)

    29. 2003
  29. "Weak finite-time Melnikov theory and viscous perturbations of 3-D Euler flows" Physica D 176 (2003) 82-106 (with S.Balasuriya and I.Mezic)
  30. "Chloropohyll dispersal by eddy-eddy interactions in the Gulf of Mexico" Journal of Geophysical Research 108 (2003) 3105-3117 (with M.Toner, A.D.Kirwan, L.Kantha and F.Muller-Kräger)
  31. "The stability of travelling calcium pulses in a pancreatic acinar cell" Physica D, 177 (2003) 242-258 (with M.Romeo)
  32. "On stratified shear flow in sea straits of arbitrary cross-scetion" Studies in Applied Math, 111 (2003) 409-434 (with J.Deng, L.Pratt and L.Howard)
  33. "A method for assimilation of Lagrangian data" Monthly Weather Review 131 (2003) 2247-2260 (with K.Ide and L.Kuznetsov)

    34. 2002
  34. "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)
  35. "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)
  36. "Drifter launch strategies based on dynamic Lagrangian templates" Journal of Physical Oceanography, 32 (2002) 1855-1869 (with A.Poje, M.Toner and A.D.Kirwan Jr.)
  37. "The Loop Current and adjacent rings delineated by Lagrangian analysis in near surface flows" Journal of Marine Research, 60 (2002) 405-429 (with L.Kuznetsov, M.Toner, A.D.Kirwan Jr., L.Kantha and J.Choi)
  38. "Pulse propagation in media with deterministic and random dispersion variations" Optics Communications, 214 (2002) 353 - 362 (with T.Schäfer and R.Moore)
  39. "Pulse stabilization by high order dispersion management" Optics Letters, 27 (2002) 1-4 (with J.Moeser and I.Gabitov)
  40. "Lagrangian data assimilation for point vortex systems" Journal of Turbulence, 3 (2002) 1-7 (with K.Ide and L.Kuznestov)

    41. 2001
  41. "Bifurcation of asymmetric solutions in nonlinear optical media" ZAMP, 52 (2001) 859-880 (with T.Küpper and K.Schaffner)
  42. "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)
  43. "Stabilizing effects of dispersion management" Physica D 152-3 (2001) 794-817 (with V.Zharnitsky, E.Grenier and S.Turitsyn)
  44. "Stability of neuronal pulses composed of two concatenated unstable kinks" Phys Rev E 63 (2001) 011904-1 (with M.Romeo)
  45. "Soliton internal modes: pure power law?" Phys Rev E, 63 (2001) 036602 (with P.Kevrekidis and T.Kapitula)
  46. "Diffusive draining and growth of eddies" Nonlinear Processes in Geophysics, 8 (2001) 241-251 (with S.Balasuriya)
  47. "Stability of multiple pulses in noisy optical fibers with phase-sensitive amplification" Optical Communications, 195 (2001) 127-139 (with R.Moore, B.Sandstede, W.Kath and J.Alexander)

    48. 2000
  48. "Bifurcation of internal solitary wave modes from the essential spectrum" Phys Rev E, 61 (2000) 3114-3121 (with P.Kevrekidis)
  49. "A spectral mapping theorem and invariant manifolds for nonlinear Schrödinger equations" Indiana U. Math. Journal, 49 (2000) 221--243 (with F.Geszetesy, Y.Latushkin and M.Stanislavova)
  50. "Instability of multiple pulses in coupled nonlinear Schrödinger equations" Phys Rev E, 61 (2000) 5886-5892 (with A.C.Yew and B.Sandstede)
  51. "Melnikov theory for finite-time vector fields" Nonlinearity, 13 (2000) 1357-1377 (with B.Sandstede, S.Balasuriya and P.Miller)
  52. "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)
  53. "Ground states of dispersion manged NLS" Phys Rev E 62 (2000) 7358 (with V.Zharnitsky, E.Grenier, J.Hesthaven and S.Turitsyn)

    54. 1999
  54. "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)
  55. "Lagrangian motion and fluid exchange in a barotropic meandering jet" Journal of Physical Oceanography, 29 (1999) 2635-2655 (with A. Rogerson, P.Miller and L.Pratt)

    56. 1998
  56. "Existence of standing pulse solutions to an inhomogeneous reaction-diffusion equation" Journal of Dynamics and Differential Equations,10 (1998) 1-35 (with J.Rubin)
  57. "Viscous perturbations of vorticity conserving flows and splitting of separatrices" Nonlinearity, 11 (1998) 47-77 (with B.Sandstede and S.Balasuriya)
  58. "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)

    59. 1997
  59. "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)
  60. "Stability of pulses on optical fibers with phase-sensitive amplifiers" ZAMP, 48 (1997) 175-192 (with J.Alexander, M.Grillakis, B.Sandstede)
  61. "Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers" Physica D, 106 (1997) 167-206 (with B.Sandstede and J.Alexander)
  62. "Phase field models for hypercooled solidification" Physica D, 104 (1997) 1-31 (with P.Bates, P.Fife and R.Gardner)
  63. "Quantifying transport in numerically generated velocity fields" Physica D, 110 (1997) 105-122 (with P.Miller, A.Rogerson and L.Pratt)
  64. "Bifurcations and edge oscillations in the semiconductor Fabry-Pérot interferometer" Optics Communications, 140 (1997) 93-98 (with J.Rubin)
  65. "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)

    66. 1996
  66. "Tracking invariant manifolds up to exponentially small errors" SIAM Journal of Math Analysis, 27 (1996) 558-577 (with T.Kaper and N.Kopell)

    67. 1995
  67. "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)
  68. "Stability of the in-phase travelling wave solution in a pair of coupld nerve fibers" Indiana University Journal of Math, 44 (1995) 189-220 (with A.Bose)
  69. "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)

    70. 1994
  70. "Tracking invariant manifolds with differential forms in singularly perturbed systems" Journal of Differential Equations, 108 (1994) 64-88 (with N.Kopell)
  71. "Existence and stability of asymptotically oscillatory double pulses," Journal für die reine und angewandte Mathematik, 446 (1994) 49-79 (with J.Alexander)
  72. "Invariant Manifolds and Singularly Perturbed Boundary Value Problems" SIAM Journal of Numerical Analysis, 31 (1994) 1558-1576 (with S.-K.Tin and N.Kopell)

    73. 1993
  73. "A geometric proof of the Kwong-McLeod uniqueness result" SIAM Journal of Math Analysis, 24 (1993) 436-443 (with C.Clemons)
  74. "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)
  75. "Existence and stability of asymptotically oscillatory triple pulses" ZAMP, 44 (1993) 189-200 (with J.Alexander)
  76. "A mechanism for capture into resonance" Physica D, 69 (1993) 85-106 (with T. Burns)

    77. 1991
  77. "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)
  78. "Stability of travelling wave solutions of diffusive predator-prey systems" Transactions of the American Mathematical Society, 377 (1991) 465-524 (with R.Gardner)
  79. "Competition between generic and non-generic fronts in envelope equations" Physical Review A, 44 (1991) 3636-3652 (with J.Powell and A.Newell)

    80. 1990
  80. "A topological invariant arising in the stability analysis of travelling waves" Journal für die reine und angewandte Mathematik, 410 (1990) 167-212 (with J.Alexander and R.Gardner)
  81. "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)

    82. 1989
  82. "Invariant manifolds for semilinear partial differential equations" Dynamics Reported, 2 (1989) 1-38 (with P.Bates)
  83. "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)

    84. 1988
  84. "Instability of standing waves for nonlinear Schrödinger type equations" Ergodic Theory and Dynamical Systems, 8 (1988) 119-138
  85. "An instability mechanism for radially symmetric standing waves of nonlinear Schrödinger equations" Journal of Differential Equations, 17 (1988) 34-62
  86. "A shooting argument with oscillation for semilinear elliptic radially symmetric equations" Proceedings of the Royal Society of Edinburgh, 108A (1988) 165-180 (with T.Küpper and H.Plakties)
  87. "Radial solutions of a semilinear elliptic equation at the critical exponent" Archive for Rational Mechanics and Analysis, 104 (1988) 251-270
  88. "Jumping stable manifolds for dissipative maps of the plane" Physica D, 35 (1988) 87-106 (with S.Hammel)

    89. 1986
  89. "On the infinitely many solutions of a semilinear elliptic equation" SIAM Journal of Math Analysis, 17 (1986) 803-835 (with T.Küpper)
  90. "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.)
  91. "Instability of standing waves in nonlinear optical waveguides" Physics Letters A, 117 (1986) 175-180 (with J.Moloney)

    92. 1985
  92. "Global dynamical behavior of the optical field in a ring cavity" Journal of the Optical Society of America B, 2 (1985) 552-564 (with S.M. Hammel and J.V. Moloney)

    93. 1984
  93. "Characterization of bifurcation from the continuous spectrum by nodal properties" Journal of Differential Equations, 45 (1984) 196-220 (with T.Küpper)
  94. "Stability of the travelling wave solution of the FitzHugh-Nagumo system" Transactions of the American Mathematical Society, 286 (1984) 431-469

    95. 1983
  95. "Spherically symmetric solutions of a reaction-diffusion equation" Journal of Differential Equations, 49 (1983) 142-169
  96. "Asymptotic behavior of a reaction-diffusion equation in higher space dimensions" Rocky Mountain Journal of Math, 13 (1983) 355-364

    97. 1981
  97. "The ρ-calculus" Zeitschr. f. math. logik und grundlagen d. math. 97 (1981) 97-110 (with P.Kelemen)
Papers in Conference Proceedings and Other Collections
  1. Spectral Stability of Combustion Fronts: Transition from High to Infinite Lewis Number. Abstract in Proceedings of Equadiff, 2007 (with A.Ghazaryan)
  2. Dynamic Consistency and Lagrangian Data in Oceanography: Mapping, Assimilation, and Optimization Schemes. Book chapter in LAPCOD, 2005 (with T.M.Chin, K.Ide, L.Kuznetsov and A.Mariano)
  3. "Random dispersion on fibers carrying optical pulses", NLGW, Stresa, Italy, September, 2002 (with T. Schäfer and R.Moore)
  4. "A Scheme for the assimilation of Lagrangian data" Proceedings of Fluid Dynamics conference, Santa Barbara, CA, March, 2002 (with K.Ide and L.Kuznetsov)
  5. "Invariant Manifolds and Lagrangian Dynamics in the Ocean and Atmosphere" Handbook of Dynamical Systems: Towards Applications, B.Fiedler ed., Elsevier, 2002 (with S.Winkler)
  6. "Dynamic Consistency and Lagrangian Data in Oceanography: Mapping, Assimilation, and Optimization Schemes" Book chapter in LAPCOD, 2001 (with T.M.Chin, K.Ide, L.Kuznetsov and A.Mariano)
  7. "A primer on the Exchange Lemma in fast-slow systems" to appear in Multiple Time Scale Dynamical Systems, IMA Proceedings, Springer-Verlag, 2000 (with T.Kaper)
  8. "Stable multiple pulses in optical fibers with phase-sensitive amplification" 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)
  9. "Chaotic mixing across oceanic jets" Proc. ONR/NUWC Conference on Nonlinear Signal Processing, Mystic, CT, July 1995 (with P.Miller, G.Haller and L.Pratt)
  10. "On the significance of homoclinic orbits to chaotic motion" in The Chaos Paradigm: Developments and Applications in Engineering and Science, R.Katz ed., Proceedings of the ONR/NUWC Conference, Mystic, CT, April 1993, AIP Conference Proceedings 296
  11. "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)
  12. "Stability of one-dimensional waves in weak and singular limits", in Viscous Profiles and Numerical Methods for Shock Waves, M.Shearer ed., SIAM Proceedings in Applied Mathematics 56, 1991 (with R.Gardner)
  13. "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)
  14. "Standing Waves of nonlinear Schrödinger equations: existence and stability" in Material Instabilities in Continuum Mechanics and Related Mathematical Problems, J.M.Ball ed., Oxford, 1988
  15. "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)
  16. "On the infinitely many standing waves of some nonlinear Schrödinger 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
  17. "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)
  18. "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
  19. "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)
Papers Submitted
  1. "Symmetry Breaking and Instability of Pulses in Nonlinearly Coupled Nonlinear Shr\"{o}dinger Equations," submitted to SIAM Journal of Dynamical Systems (with R.Jackson)
  2. "Capturing Deviation from Ergodicity Across Scales", submitted to Phsyica D (with S.Scott, L.Kuznetsov. T.Redd and I.Mezic)
  3. "Traveling waves in porous media combustion: uniqueness of waves for small thermal diffusivity", submitted to JDDE (with A.Ghazaryan and P.Gordon)
  4. "The role of flow geometry in Lagrangian data assimilation", submitted to Tellus (with H.Salman and K.Ide)
  5. "Solitary waves of the regularized short pulse and Ostrovsky equations", submitted to SIMA (with N. Costanzino and V. Manukian)
Lecture Notes
  1. "Geometric Singular Perturbation Theory" C.I.M.E. Lectures, Montecatini Terme, June 1994, Lecture Notes in Mathematics 1609, Springer-Verlag, Heidelberg, 1995
Edited Volumes
  1. Multiple Time Scale Dynamical Systems, IMA Proceedings vol. 122, Springer-Verlag, NY, 2000 (with A.Khibnik)
  2. Dynamics Reported (New Series) Expositions in Dynamical Systems, Volumes I-IV, Springer-Verlag 1991-5 (with H.-O. Walther and U. Kirchgraber)
Other Publications
  1. "Climate change: can mathematics help clear the air?" Opinion Column in Notices AMS April (2009)
  2. "Is Mathematics misapplied in the environment?" Book Review in Notices AMS April (2008)
  3. "A Rational Approach to Earth Management" SIAM News July/August 2001
  4. "Whither Applied Nonlinear Dynamics" Mathematics Unlimited: 2001 and Beyond, Vol. II, Springer-Verlag
  5. "A Dynamics Group Looks at the Ocean" SIAM News, March, 2000
  6. "Lagrangian Predictability in Ocean Flows" in ONR report based on DRI Workshop, Nice, May 2000
  7. "A geometric approach to systems with multiple time scales" Journal of the Japanese SIAM, 7 (1997) 39-48 (in Japanese-translated by K.Sakamoto)
  8. "Settling and chaotic mixing in oceanic flows: the rôle of heteroclinic orbits", Naval Research Reviews, Office of Naval research, 46 (1995) 17-28 (with G.Haller, P.D.Miller and J.Rubin)
  9. Dynamical Systems at ICIAM 1991, SIAM\ News, October, 1991