Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

Abstract A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a ( 3 + 1 ) -dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed.

[1]  Jingsong He,et al.  Rogue Waves of the Fokas–Lenells Equation , 2012, 1209.5540.

[2]  V. Matveev,et al.  Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation , 2011 .

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

[4]  Zhenyun Qin,et al.  Matter rogue waves in an F=1 spinor Bose-Einstein condensate. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Adrian Ankiewicz,et al.  Discrete rogue waves of the Ablowitz-Ladik and Hirota equations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Yasuhiro Ohta,et al.  Rogue waves in the Davey-Stewartson I equation. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Zhenya Yan,et al.  Nonautonomous "rogons" in the inhomogeneous nonlinear Schrödinger equation with variable coefficients , 2010, 1009.3731.

[8]  Kharif Christian,et al.  Rogue Waves in the Ocean , 2009 .

[9]  U. Bandelow,et al.  Sasa-Satsuma equation: soliton on a background and its limiting cases. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Xianguo Geng,et al.  N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation , 2007 .

[11]  Suotang Jia,et al.  Peregrine rogue waves induced by the interaction between a continuous wave and a soliton. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  B. Guo,et al.  Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schrödinger Equations , 2011 .

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

[14]  Q. P. Liu,et al.  Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Abdul-Majid Wazwaz,et al.  A (3 + 1)-dimensional nonlinear evolution equation with multiple soliton solutions and multiple singular soliton solutions , 2009, Appl. Math. Comput..

[16]  Lihong Wang,et al.  Breather and rogue wave solutions of a generalized nonlinear Schrödinger equation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Zhaqilao,et al.  Positon, Negaton, Soliton and Complexiton Solutions to a Four-Dimensional Nonlinear Evolution Equation , 2009 .

[18]  Zhaqilao,et al.  DARBOUX TRANSFORMATION AND VARIOUS SOLUTIONS FOR A NONLINEAR EVOLUTION EQUATION IN (3 + 1)-DIMENSIONS , 2008 .

[19]  Zhaqilao.  On Nth-order rogue wave solution to nonlinear coupled dispersionless evolution equations , 2012 .

[20]  Z. Dai,et al.  New Rogue Wave Solutions of (1+2)-Dimensional Non-Isospectral KP-II Equation , 2013 .

[21]  Xianguo Geng,et al.  Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations , 2003 .

[22]  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.

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

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

[25]  Jingsong He,et al.  Rogue waves of the Hirota and the Maxwell-Bloch equations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Vladimir V. Konotop,et al.  Vector rogue waves in binary mixtures of Bose-Einstein condensates , 2010 .

[27]  Adrian Ankiewicz,et al.  Rogue waves, rational solutions, the patterns of their zeros and integral relations , 2010 .

[28]  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.

[29]  A. Fokas,et al.  Generating mechanism for higher-order rogue waves. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Zhaqilao.  On Nth-order rogue wave solution to the generalized nonlinear Schrödinger equation , 2013 .

[31]  Willy Hereman,et al.  Symbolic methods to construct exact solutions of nonlinear partial differential equations , 1997 .

[32]  Adrian Ankiewicz,et al.  Rogue wave triplets , 2011 .

[33]  Jingsong He,et al.  The rogue wave and breather solution of the Gerdjikov-Ivanov equation , 2011, 1109.3283.

[34]  Guiqiong Xu,et al.  The soliton solutions, dromions of the Kadomtsev–Petviashvili and Jimbo–Miwa equations in (3 + 1)-dimensions , 2006 .

[35]  Elena Magliaro,et al.  Emergence of gravity from spinfoams , 2011, 1108.2258.

[36]  Jingsong He,et al.  The Darboux transformation of the derivative nonlinear Schrödinger equation , 2011, 1109.0674.

[37]  N. Akhmediev,et al.  Are rogue waves robust against perturbations , 2009 .

[38]  Yasuhiro Ohta,et al.  Dynamics of rogue waves in the Davey–Stewartson II equation , 2012, 1212.0152.

[39]  Jingsong He,et al.  Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative , 2012, 1202.0356.

[40]  Peter A. Clarkson,et al.  Rational Solutions Of The Boussinesq Equation , 2008 .

[41]  Jingsong He,et al.  Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Wei-Guo Zhang,et al.  Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations , 2013 .

[43]  Zhaqilao.  Nth-order rogue wave solutions of the complex modified Korteweg–de Vries equation , 2013 .