Rogue Wave Modes for the Long Wave–Short Wave Resonance Model

The long wave–short wave resonance model arises physically when the phase velocity of a long wave matches the group velocity of a short wave. It is a system of nonlinear evolution equations solvable by the Hirota bilinear method and also possesses a Lax pair formulation. ‘‘Rogue wave’’ modes, algebraically localized entities in both space and time, are constructed from the breathers by a singular limit involving a ‘‘coalescence’’ of wavenumbers in the long

[1]  K. Chow,et al.  Coalescence of Wavenumbers and Exact Solutions for a System of Coupled Nonlinear Schrödinger Equations , 1998 .

[2]  S. A. Dyer,et al.  The bilinear transformation , 2000 .

[3]  John Grue,et al.  Long time interaction of envelope solitons and freak wave formations , 2006 .

[4]  Karlsson,et al.  Interactions between polarized soliton pulses in optical fibers: Exact solutions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Adrian Ankiewicz,et al.  Second-order nonlinear Schrödinger equation breather solutions in the degenerate and rogue wave limits. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  V. Ruban.  Two different kinds of rogue waves in weakly crossing sea states. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  M. Funakoshi.  Steady Trapped Solutions to Forced Long-Short Interaction Equation , 1993 .

[8]  Alexey Slunyaev.  Nonlinear analysis and simulations of measured freak wave time series , 2006 .

[9]  K. Porsezian,et al.  New Types of Rogue Wave in an Erbium-Doped Fibre System , 2012 .

[10]  C. M. Schober,et al.  Melnikov analysis and inverse spectral analysis of rogue waves in deep water , 2006 .

[11]  A. Noguchi,et al.  Dark Soliton in Long and Short Wave Resonant Interaction , 1980 .

[12]  Efim Pelinovsky,et al.  Numerical modeling of the KdV random wave field , 2006 .

[13]  M. Wadati,et al.  The Multiple Pole Solutions of the Sine-Gordon Equation , 1984 .

[14]  V. Zakharov,et al.  Freak waves as nonlinear stage of Stokes wave modulation instability , 2006 .

[15]  Harald E. Krogstad,et al.  Oceanic Rogue Waves , 2008 .

[16]  松野 好雅,et al.  Bilinear transformation method , 1984 .

[17]  B. Guo,et al.  Homoclinic orbits for the coupled nonlinear Schrödinger system and long–short wave equation ☆ , 2005 .

[18]  Yasuhiro Ohta,et al.  General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[19]  Luigi Cavaleri,et al.  Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves , 2006 .

[20]  K. Konno,et al.  N Double Pole Solution for the Modified Korteweg-de Vries Equation by the Hirota's Method , 1989 .

[21]  Kenji Ohkuma,et al.  Multiple-Pole Solutions of the Modified Korteweg-de Vries Equation , 1982 .

[22]  Yuri S. Kivshar,et al.  Optical Solitons: From Fibers to Photonic Crystals , 2003 .

[23]  O. C. Wright.  Homoclinic Connections of Unstable Plane Waves of the Long‐Wave–Short‐Wave Equations , 2006 .

[24]  J. Soto-Crespo,et al.  Rogue waves and rational solutions of the nonlinear Schrödinger equation. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  M. Okamura,et al.  Two-Dimensional Resonant Interaction between Long and Short Waves , 1989 .

[26]  T. Kakutani,et al.  Solitary and E-Shock Waves in a Resonant System between Long and Short Waves , 1994 .

[27]  K. Chow.  Solitary Waves on a Continuous Wave Background , 1995 .

[28]  K. Chow,et al.  Coalescence of Ripplons, Breathers, Dromions and Dark Solitons , 2001 .

[29]  A. Craik,et al.  Wave Interactions and Fluid Flows , 1986 .