Darboux transformation and dark rogue wave states arising from two-wave resonance interaction

Abstract Exact rogue wave solutions of the long wave–short wave resonance equation are obtained via Darboux transformations. Compared to the real long-wave field which always features a single hump structure, the short-wave field can be manifested as bright rogue wave, intermediate rogue wave, or dark rogue wave, depending on the subtle nonlinearity driven by the long-wave field.

[1]  Günther Clauss,et al.  Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test , 2013, PloS one.

[2]  M. Shats,et al.  Capillary rogue waves. , 2010, Physical review letters.

[3]  N. Akhmediev,et al.  Modulation instability and periodic solutions of the nonlinear Schrödinger equation , 1986 .

[4]  E. Pelinovsky,et al.  Extreme ocean waves , 2008 .

[5]  Fabio Baronio,et al.  Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves. , 2012, Physical review letters.

[6]  Yan‐Chow Ma.  The Complete Solution of the Long‐Wave–Short‐Wave Resonance Equations , 1978 .

[7]  Yan‐Chow Ma,et al.  The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation , 1979 .

[8]  Uwe Bandelow,et al.  Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa-Satsuma case , 2012 .

[9]  T. Maimbourg,et al.  Oscillon dynamics and rogue wave generation in Faraday surface ripples. , 2012, Physical review letters.

[10]  Ricardo Sevilla-Escoboza,et al.  Rogue waves in a multistable system. , 2011, Physical review letters.

[11]  Shihua Chen.  Twisted rogue-wave pairs in the Sasa-Satsuma equation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[13]  R Sevilla-Escoboza,et al.  Multistate intermittency and extreme pulses in a fiber laser. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  N. Akhmediev,et al.  Waves that appear from nowhere and disappear without a trace , 2009 .

[15]  D. H. Peregrine,et al.  Water waves, nonlinear Schrödinger equations and their solutions , 1983, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[16]  Fabio Baronio,et al.  Rogue waves emerging from the resonant interaction of three waves. , 2013, Physical review letters.

[17]  Kwok Wing Chow,et al.  Rogue Wave Modes for the Long Wave–Short Wave Resonance Model , 2013 .

[18]  D. J. Benney.  A General Theory for Interactions Between Short and Long Waves , 1977 .

[19]  Frédéric Dias,et al.  The Peregrine soliton in nonlinear fibre optics , 2010 .

[20]  Umberto Bortolozzo,et al.  Rogue waves and their generating mechanisms in different physical contexts , 2013 .

[21]  P. Grelu,et al.  Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser. , 2012, Physical review letters.

[22]  Adrian Ankiewicz,et al.  Rogue waves and rational solutions of the Hirota equation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Pierre Suret,et al.  Experimental evidence of extreme value statistics in Raman fiber lasers. , 2012, Optics letters.

[25]  N. Hoffmann,et al.  Rogue wave observation in a water wave tank. , 2011, Physical review letters.

[26]  Shihua Chen,et al.  Rogue waves in coupled Hirota systems , 2013 .

[27]  Nail Akhmediev,et al.  Dissipative rogue waves: extreme pulses generated by passively mode-locked lasers. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Yuri S. Kivshar,et al.  Dark optical solitons: physics and applications , 1998 .

[29]  Y. Nakamura,et al.  Observation of Peregrine solitons in a multicomponent plasma with negative ions. , 2011, Physical review letters.

[30]  L. Redekopp,et al.  On two-dimensional packets of capillary-gravity waves , 1977, Journal of Fluid Mechanics.

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

[32]  Cristina Masoller,et al.  Deterministic optical rogue waves. , 2011, Physical review letters.