Publications (in reverse chronological order of first submission)

  1. The explicit solution of linear, dissipative, second-order initial-boundary value problems with variable coefficients (with M. Farkas), (submitted for publication, 2024) .pdf
  2. Selfsimilarity and recurrence in stability spectra of near-extreme Stokes waves (with S. Dyachenko, \& A. Semenova), (submitted for publication, 2024) .pdf
  3. The instability of near-extreme Stokes waves (with S. Dyachenko, P. Lushnikov \& A. Semenova), (submitted for publication, 2022) .pdf
  4. Solving the heat equation with variable thermal conductivity (with M. Farkas), (submitted for publication, 2022) .pdf
  5. The analytic extension of solutions to initial-boundary value problems outside their domain of definition (with M. Farkas and J. Cisneros), (submitted for publication, 2022) .pdf
  6. A High-Order Asymptotic Analysis of the Benjamin-Feir Instability Spectrum in Arbitrary Depth (with R. Creedon), (submitted for publication, 2022) .pdf
  7. The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method (with J. Cisneros), (submitted for publication, 2021) .pdf
  8. High-Frequency Instabilities of Stokes Waves (with R. Creedon and O. Trichtchenko), (accepted for publication, JFM, 2021) .pdf (Note: the full submission, including Mathematica files, can be found on the arxiv)
  9. The numerical unified transform method for the nonlinear Schrodinger equation on the half line (with X. Yang and T. Trogdon), (submitted for publication, 2021) .pdf.
  10. The numerical solutions of linear semi-discrete evolution problems on the half-line using the Unified Transform Method (with J. Cisneros), (submitted for publication, 2021) .pdf.
  11. High-Frequency Instabilities of a Boussinesq-Whitham equation: A Perturbative Approach (with R. Creedon and O. Trichtchenko), (submitted for publication, 2021) .pdf.
  12. High-Frequency Instabilities of the Kawahara Equation: A Perturbative Approach (with R. Creedon and O. Trichtchenko), (submitted for publication, 2021) .pdf.
  13. Stability of elliptic solutions to the sinh-Gordon equation (with Wen-Rong Sun), (submitted for publication, 2020) .pdf.
  14. The implementation of the Unified Transform to the Nonlinear Schr\"odinger equation with periodic initial conditions. (with A. S. Fokas and J. Lenells), (submitted for publication, 2020) .pdf.
  15. The Numerical Unified Transform Method for initial-boundary value problems on the half line. (with T. Trogdon and X. Yang), (IMA Journal of Numerical Analysis, 2021) .pdf.
  16. Real Lax Spectrum Implies Spectral Stability (with J. Upsal), (submitted for publication, 2019) .pdf.
  17. The orbital stability of elliptic solutions of the Focusing Nonlinear Schrodinger Equation (with J. Upsal), SIAM Journal of Mathematical Analysis 52, 1-41. .pdf.
  18. Numerical inverse scattering for the sine-Gordon equation (with X. Yang and T. Trogdon), (submitted for publication, 2018) .pdf.
  19. Stability of periodic traveling wave solutions to the Kawahara equation (with O. Trichtchenko and R. Kollar), (submitted for publication, 2018) .pdf.
  20. Direct Characterization of spectral stability of small amplitude periodic waves in scalar problems via dispersion relation (with R. Kollar and O. Trichtchenko), (submitted for publication, 2018) .pdf.
  21. On the nonintegrability of equations for long- and short-wave interactions (with J. Upsal), (submitted for publication, 2017) .pdf.
  22. The time-dependent Schrodinger equation with piecewise constant potentials (with N. Sheils), (submitted for publication, 2017) .pdf.
  23. The stability spectrum for elliptic solutions to the sine-Gordon equation (with P. McGill and Benjamin Segal) (Submitted for publication, 2017) .pdf.
  24. Fokas's Unified Transform Method for Linear Systems (with Q. Guo, Eli Shlizerman and V. Vasan) (Submitted for publication, 2017) .pdf.
  25. The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation (with B. Segal) (Submitted for publication, 2016) .pdf.
  26. Explicit solutions for a long-wave model with constant vorticity (with B. Segal, D. Moldabayev and H. Kalisch ) (Submitted for publication, 2016) .pdf.
  27. The interaction of long and short waves in dispersive media (with N. Nguyen and B. Segal ) Journal of Physics A, 415501, 2016 .pdf.
  28. The instability of Wilton ripples (with O. Trichtchenko and J. Wilkening ) (Submitted for publication, 2015) .pdf.
  29. The linear KdV equation with an interface (with N. Sheils and D. A. Smith ) (Submitted for publication, 2015) .pdf.
  30. Initial-to-Interface Maps for the Heat Equation on Composite Domains (with N. Sheils ) (Submitted for publication, 2015) .pdf.
  31. High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs (with O. Trichtchenko ) (Submitted for publication, 2015) .pdf.
  32. A method to recover water-wave profiles from pressure measurements (with V. Vasan, K. Oliveras, D. Henderson) (Submitted for publication, 2015) .pdf.
  33. Computing the Riemann Constant Vector (with C. Swierczewski) (Submitted for publication, 2015) .pdf.
  34. Heat conduction on the ring. Interface problems with periodic boundary conditions. (with N. E. Sheils) (Submitted for publication, 2014) .pdf.
  35. Interface Problems for Dispersive Equations (with N. E. Sheils) (Submitted for publication, 2014) .pdf.
  36. Stability of gravity waves in the presence of surface tension (with O. Trichtchenko) (Submitted for publication, 2013) .pdf.
  37. Non-steady state heat conduction in composite walls (with B. Pelloni and N. E. Sheils) (Submitted for publication, 2013) .pdf.
  38. Short-wave transverse instabilities of line solitons of the 2-D hyperbolic nonlinear Schrodinger equation (with D. E. Pelinovsky, E. A. Ruvinsakaya and O. A. Kurkina) (Theoretical and Mathematical Physics 179, pp 452--461, 2014) .pdf (English), .pdf (Russian).
  39. Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results (with Tom Trogdon) (Submitted for publication, 2013) .pdf.
  40. A numerical dressing method for the nonlinear superposition of solutions of the KdV equation (with Tom Trogdon) (Submitted for publication, 2013) .pdf.
  41. On the spectral stability of solitary wave solutions of the vector NLS equation (with Natalie Sheils, Nghiem V. Nguyen, Rushun Tian) (Submitted for publication, 2013) .pdf.
  42. The bernoulli boundary condition for traveling water waves (with Vishal Vasan) (Accepted for publication, Applied Mathematics Letters, 2012) .pdf.
  43. Neck instability of bright solitary waves in hyperbolic Kerr media (with Simon-Pierre Gorza, Tom Trogdon, Philippe Emplit, Marc Haelterman) (Submitted for publication) .pdf.
  44. Numerical computation of the finite-genus solutions of the Korteweg-de Vries equation via Riemann-Hilbert problems (with Tom Trogdon) (Accepted for publication, Applied Mathematics Letters, 2012) .pdf.
  45. Relating the bottom pressure and the surface elevation in the water wave problem (with Katie Oliveras and Vishal Vasan) (Submitted for publication) .pdf.
  46. A Riemann-Hilbert problem for the finite-genus solutions of the KdV equation and its numerical solution (with Tom Trogdon) (Submitted for publication) .pdf.
  47. Global existence for a coupled system of Schrodinger equations with power-type nonlinearities (with Nghiem V. Nguyen, Rushun Tian, and Natalie Sheils) (J. Math. Phys. 54, 011503, 2013) .pdf.
  48. The inverse water wave problem of bathymetry detection (with Vishal Vasan) (Submitted for publication) .pdf.
  49. Computing Riemann Theta functions in Sage with applications (with Chris Swierczewski) (Submitted for publication) .pdf.
  50. Recovering the water-wave profile from pressure measurements (with Katie Oliveras, Vishal Vasan, and Diane Henderson) (Submitted for publication) .pdf.
  51. Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations (with Thomas Trogdon and Sheehan Olver) (Submitted for publication) .pdf.
  52. Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation (with Vishal Vasan) (Submitted for publication) .pdf.
  53. The instabilities of periodic traveling water waves with respect to transverse perturbations (with Katie Oliveras) (Submitted for publication) .pdf.
  54. Recovering the water-wave surface from pressure measurements (with Diane Henderson, Katie Oliveras, and Vishal Vasan) (Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves (Refereed), WAVES 2011, Vancouver July 25-29, 2011) .pdf.
  55. Solving linear partial differential equations (with Thomas Trogdon and Vishal Vasan) (SIAM Review 56, 159--186) .pdf.
  56. Experimental demonstration of the oscillatory snake instability of the bright soliton of the (2+1)D hyperbolic nonlinear Schrodinger equation (with Simon-Pierre Gorza, Philippe Emplit, Thomas Trogdon, and Marc Haelterman) (Physical Review Letters 106, 094101, 2011) .pdf.
  57. The solution of linear constant-coefficient evolution PDEs with periodic boundary conditions (with Thomas Trogdon) (Accepted for publication, Applicable analysis) .pdf.
  58. The stability analysis of the periodic traveling wave solutions of the mKdV equation (with Michael Nivala) (Studies in Applied Mathematics 126, 17-48, 2010) .pdf.
  59. Transverse instability of bright solitons in hyperbolic dispersive media (with Simon-Pierre Gorza, Philippe Emplit, Marc Haelterman, and Thomas Trogdon) (Proceedings of the 2010 Nonlinear Photonics meeting (refereed) in Karlsruhe, Germany) .pdf.
  60. The orbital stability of the cnoidal waves of the Korteweg-de Vries equation (with Todd Kapitula) (Physics Letters A 374, 4018-4022, 2010) .pdf.
  61. The instability of periodic surface gravity waves (with Katie Oliveras) (Journal of Fluid Mechanics 675, 141-167, 2011) .pdf.
  62. Elliptic solutions of the defocusing NLS equation are stable (with Nate Bottman and Michael Nivala) (Journal of Physics A 44, 285201, 2011) .pdf.
  63. On the orbital (in)stability of spatially periodic stationary solutions of generalized Korteweg-de Vries equations (with Todd Kapitula) (submitted for publication) .pdf.
  64. Spectral stability of stationary solutions of a Boussinesq system describing long waves in dispersive media (with Min Chen, Chris Curtis, Crystal Lee, and Nghiem Nguyen) (SIAM J. Applied Dynamical Systems 9, 999-1018, 2010) .pdf.
  65. Periodic finite-genus solutions of the KdV equation are orbitally stable (with Michael Nivala) (Physica D 239, 1147-1158, 2010) .pdf .
  66. Data analysis and reduction using stationary solutions of the NLS equation (with David Lovit) (Applicable Analysis 89, 611-626, 2010) .pdf .
  67. On the convergence of Hill's method (with Chris Curtis) (Mathematics of Computation 79, 169-187, 2010) .pdf .
  68. KdV cnoidal waves are linearly stable (with Nate Bottman) (DCDS-A 25, 1163-1180, 2009) .pdf .
  69. Computing the Abel map (with Matt Patterson) (Physica D 237, 3214-3232, 2008) .pdf .
  70. Symbolic integration and summation using homotopy methods (with Michael Nivala) (Mathematics and Computers in Simulation 80, 825-836, 2009) .pdf .
  71. The pole dynamics of rational solutions of the viscous Burgers equation (with Yoshifumi Kimura and Harvey Segur) Journal of Physics A 40, 5459-5467, 2007. .pdf .
  72. Continuous and Discrete Homotopy Operators: A Theoretical Approach made Concrete (with Willy Hereman and L. D. Poole) (Mathematics and Computers in Simulation 74, 2007, 352-360) .pdf .
  73. SpectrUW: a laboratory for the numerical exploration of spectra of linear operators (with Firat Kiyak, J. D. Carter and J. Nathan Kutz ) (Mathematics and Computers in Simulation 74, 2007, 370-379) .pdf .
  74. Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schr\"odinger equation (with R. J. Thelwell and J. D. Carter) (Journal of Physics A 39, 73-84, 2006) .pdf .
  75. Instabilities of one-dimensional trivial-phase solutions of the two-dimensional cubic nonlinear Schr\"odinger equation (with J. D. Carter) (Physica D 214, 42-54, 2006) .pdf .
  76. Transverse instabilities of deep-water solitary waves (with D. E. Pelinovsky and J. D. Carter) (Proceedings of the Royal Society A 462, 2039-2061, 2006) .pdf .
  77. Computing spectra of linear operators using the Floquet-Fourier-Hill method (with J. Nathan Kutz) (J. Comp. Physics 219, 296-321, 2006) .pdf .
  78. Linearly coupled Bose-Einstein Condensates: from Rabi oscillations and quasi-periodic solutions to sloshing domain walls and spiral waves (with P. G. Kevrekidis, H. E. Nistazakis, and D. J. Frantzeskakis) (Phys. Rev. A 70, 063605, 2004) .pdf .
  79. Exact nonstationary solutions of the mean-field equations of motion for two-component Bose-Einstein condensates in periodic potentials (with R. M. Bradley and J. Nathan Kutz), (J. Phys. A 38, 2005, 1901-1916) .pdf .
  80. Dynamics of periodic multi-components Bose-Einstein condensates (with J. Nathan Kutz, Matthew S. Patterson, Brandon W. Warner ) (Journal of Physics A 36, 2003, 531-547) .pdf .
  81. Singular instability of exact stationary solutions of the nonlocal Gross-Pitaeskii equation (with J. Nathan Kutz) (Physics Letters A 319, 2003, 97-103) .pdf .
  82. Computing Riemann Theta Functions ( With Matthias Heil, Alexander Bobenko, Mark van Hoeij and Markus Schmies ) (Mathematics of Computation 73 (2004) 1417-1442) .pdf .
  83. Dynamics and Stability of Bose-Einstein Condensates: the Nonlinear Schrodinger Equation with Periodic Potential (with Bela A. Frigyik and J. Nathan Kutz ) (J. Nonlinear Sci 12, pp 169-205, 2002) .pdf .
  84. Stability of exact solutions of the defocusing nonlinear Schrodinger equation with periodic potential in two dimensions (with Bela A. Frigyik and J. Nathan Kutz ) (Physics Letters A 283, 2001, pp 177-184) .pdf .
  85. Stability of Attractive Bose-Einstein Condensates in a Periodic Potential (with Jared C. Bronski, Lincoln D. Carr, Ricardo Carretero-Gonzalez, J. Nathan Kutz and K. Promislow ) (Physical Review E 64, 2001 Ref. Nr. 056615) .pdf .
  86. Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential (with Jared C. Bronski, Lincoln D. Carr, J. Nathan Kutz and K. Promislow ) (Physical Review E 63, 2001, Ref. nr. 036612) .pdf .
  87. Bose-Einstein condensates in standing waves: the cubic nonlinear Schrodinger equation with a periodic potential (with Jared C. Bronski, Lincoln D. Carr and J. Nathan Kutz ) (Physical Review Letters 86, 2001, pp 1402-1405) .pdf .
  88. Computing Riemann matrices of algebraic curves (with Mark van Hoeij ) (Physica D 152-153, 2001, pp 28-46) .pdf . (Note: this is a slightly different version from the one that is published. In my opinion this version is better.)
  89. Pole dynamics for elliptic solutions of the KdV equation (with Harvey Segur ) (Mathematical Physics, Analysis and Geometry 3, 2000, pp 49-74) .pdf .
  90. Canonical variables for multiphase solutions of the KP equation (Studies in Applied Mathematics 104, 2000, pp 229-292) .pdf .
  91. The KP equation with quasiperiodic initial data (with Harvey Segur) (Physica D 123, 1998, pp 123-152) .pdf .
  92. A constructive test for the integrability of semi-discrete systems (Physics Letters A 223, 1996, pp 45-54) .pdf.
  93. Oblique nonlinear Alfven waves in strongly magnetized beam plasmas. Part 2. soliton solutions and integrability (with Peter Meuris and Frank Verheest) (Journal of Plasma Physics 50, part 3, 1993, pp 457-476) abstract , (Electronic version of this paper is not available)
  94. Oblique nonlinear Alfven waves in strongly magnetized beam plasmas. Part 1. Nonlinear vector evolution equation (with Peter Meuris and Frank Verheest) (Journal of Plasma Physics 50, part 3, 1993, pp 445-455) abstract , (Electronic version of this paper is not available)

Contributions to books

  1. Computing with Riemann Surfaces: the algorithms of the Maple package ``algcurves'', in Lecture Notes in Mathematics, Volume 2013, Alexander Bobenko and Christian Klein, editors, Springer, 2011. .pdf (not refereed)
  2. Multidimensional Theta Functions, in the Digital Library of Mathematical Functions, National Institute for Standards and Technology, F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, editors, Cambridge University Press, 2010. (refereed).
  3. Continuous and Discrete Homotopy Operators with Applications in Integrability Testing (with W. Hereman, M. Colagrosso, R. Sayers, A. Ringler, M. Nivala and M. Hickman) in Differential Equations with Symbolic computation, edited by Dongming Wang and Zhiming Zheng, Birkhauser, 2005. .pdf (refereed).
  4. Encyclopedia of Nonlinear Science (Routhledge Publishers, 2004): entries on Kadomtsev-Petviashvili equation, Periodic Spectral theory, Poisson Brackets (not refereed).
Department of Applied Mathematics, University of Washington, Lewis Hall #202, Box 353925, Seattle, WA 98195-3925 USA
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