W-shaped soliton complexes and rogue-wave pattern transitions for the AB system

Abstract With the help of a general Nth-order rogue wave solution in a compact determinant form for the AB system, we illuminate that, by suitably choosing the wavenumber and frequency of the background wave of the component A, W-shaped soliton complex containing a fixed number of algebraic solitons merging or separating with each other exists in the component A, and rogue-wave pattern transition between the four-petaled structure and dark structure occurs in the component B. The more complicated rogue-wave pattern transitions due to the nonlinear superposition corresponding to the higher-order four-petaled rogue waves and higher-order dark rogue waves of fundamental, triangular and circular dynamical structures up to third order are demonstrated, respectively. The spectrum properties which are related to the rogue-wave pattern transitions are revealed.

[1]  Adrian Ankiewicz,et al.  Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  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.

[3]  B. Tian,et al.  Double-Wronskian solitons and rogue waves for the inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma , 2014 .

[4]  Boling Guo,et al.  High-order rogue waves in vector nonlinear Schrödinger equations. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  J. Pedlosky.  Finite-Amplitude Baroclinic Wave Packets , 1972 .

[6]  Shihua Chen,et al.  Watch-hand-like optical rogue waves in three-wave interactions. , 2015, Optics express.

[7]  Yong Chen,et al.  Generalized Darboux transformation and localized waves in coupled Hirota equations , 2013, 1312.3436.

[8]  Zhenya Yan,et al.  Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation. , 2015, Chaos.

[9]  Jeremiah D. Williams.  Plasma physics: Rogue waves caught in 3D , 2016 .

[10]  K. Chow,et al.  A coupled "AB" system: Rogue waves and modulation instabilities. , 2015, Chaos.

[11]  A. Osborne,et al.  Freak waves in random oceanic sea states. , 2001, Physical review letters.

[12]  Li-Chen Zhao,et al.  Rogue-wave pattern transition induced by relative frequency. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  N. Akhmediev,et al.  Higher-order integrable evolution equation and its soliton solutions , 2014 .

[14]  Hui-Qin Hao,et al.  Dynamic behaviors of the breather solutions for the AB system in fluid mechanics , 2013 .

[15]  John M. Dudley,et al.  Rogue wave early warning through spectral measurements , 2011 .

[16]  A Ankiewicz,et al.  Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  E. Pelinovsky,et al.  On shallow water rogue wave formation in strongly inhomogeneous channels , 2016 .

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

[19]  Xin Wang,et al.  Higher-order rogue wave solutions of the Kundu–Eckhaus equation , 2014 .

[20]  N. Akhmediev,et al.  Multi-soliton complexes. , 2000, Chaos.

[21]  A. Kamchatnov,et al.  PERIODIC SOLUTIONS AND WHITHAM EQUATIONS FOR THE AB SYSTEM , 1995 .

[22]  Wen-Li Yang,et al.  State transition induced by higher-order effects and background frequency. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  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.

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

[25]  Wen-Li Yang,et al.  Transition, coexistence, and interaction of vector localized waves arising from higher-order effects , 2015 .

[26]  John P. Boyd,et al.  Envelope Solitary Waves and Periodic Waves in the AB Equations , 2002 .

[27]  Dumitru Mihalache,et al.  Vector rogue waves in the Manakov system: diversity and compossibility , 2015 .

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

[29]  V. Konotop,et al.  Matter rogue waves , 2009 .

[30]  J. Gibbon,et al.  Solitons and Nonlinear Wave Equations , 1982 .