A second-order three-wave interaction system and its rogue wave solutions

被引：13
作者：
Geng, Xianguo [1 ]
Li, Yihao [1 ]
Xue, Bo [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, 100 Kexue Rd, Zhengzhou 450001, Henan, Peoples R China
来源：
NONLINEAR DYNAMICS | 2021年 / 105卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Second-order three-wave interaction system; Darboux transformation; Rogue wave solutions; QUASI-PERIODIC SOLUTIONS; STEEPEST DESCENT METHOD; RESONANT INTERACTION; INTERACTION EQUATIONS; ASYMPTOTICS; SOLITONS;
D O I：
10.1007/s11071-021-06727-2
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
On the basis of a 3 x 3 matrix spectral problem, a second-order three-wave interaction system is proposed. A one-fold Darboux transformation is derived by using the gauge transformation between the 3x3 matrix spectral problems. The compact determinant form of the N-fold Darboux transformation is obtained by iterating the onefold Darboux transformation and solving a complex linear algebraic system. Furthermore, the N-fold Darboux transformation and Taylor expansion are used to construct multifold generalized Darboux transforms of the second-order three-wave interaction system. As applications, the solutions of the interaction between a dark-bright soliton and a rogue wave (RW), the solutions of the interaction between two dark-bright solitons and a second-order rogue wave, the solutions of the eye-shaped rogue wave and triangle rogue wave are obtained.
引用
收藏
页码：2575 / 2593
页数：19
相关论文
共 44 条
[1]   Three-wave trapponic solitons for tunable high-repetition rate pulse train generation [J].
Baronio, Fabio ;
Conforti, Matteo ;
Degasperis, Antonio ;
Wabnitz, Stefan .
IEEE JOURNAL OF QUANTUM ELECTRONICS, 2008, 44 (5-6) :542-546
[2]   Rogue Waves Emerging from the Resonant Interaction of Three Waves [J].
Baronio, Fabio ;
Conforti, Matteo ;
Degasperis, Antonio ;
Lombardo, Sara .
PHYSICAL REVIEW LETTERS, 2013, 111 (11)
[3]   Frequency Generation and Solitonic Decay in Three Wave Interactions [J].
Baronio, Fabio ;
Conforti, Matteo ;
Andreana, Marco ;
Couderc, Vincent ;
De Angelis, Costantino ;
Wabnitz, Stefan ;
Barthelemy, Alain ;
Degasperis, Antonio .
OPTICS EXPRESS, 2009, 17 (16) :13889-13894
[4]   Semiclassical Soliton Ensembles for the Three-Wave Resonant Interaction Equations [J].
Buckingham, R. J. ;
Jenkins, R. M. ;
Miller, P. D. .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017, 354 (03) :1015-1100
[5]   Novel solution of the system describing the resonant interaction of three waves [J].
Calogero, F ;
Degasperis, A .
PHYSICA D-NONLINEAR PHENOMENA, 2005, 200 (3-4) :242-256
[6]   Inelastic scattering and interactions of three-wave parametric solitons [J].
Conforti, Matteo ;
Baronio, Fabio ;
Degasperis, Antonio ;
Wabnitz, Stefan .
PHYSICAL REVIEW E, 2006, 74 (06)
[7]   Modulational instability of dark solitons in three wave resonant interaction [J].
Conforti, Matteo ;
Baronio, Fabio ;
Degasperis, Antonio .
PHYSICA D-NONLINEAR PHENOMENA, 2011, 240 (17) :1362-1369
[8]   Exact solutions of the 3-wave resonant interaction equation [J].
Degasperis, A ;
Lombardo, S .
PHYSICA D-NONLINEAR PHENOMENA, 2006, 214 (02) :157-168
[9]   Rational solitons of wave resonant-interaction models [J].
Degasperis, Antonio ;
Lombardo, Sara .
PHYSICAL REVIEW E, 2013, 88 (05)
[10]   A STEEPEST DESCENT METHOD FOR OSCILLATORY RIEMANN-HILBERT PROBLEMS - ASYMPTOTICS FOR THE MKDV EQUATION [J].
DEIFT, P ;
ZHOU, X .
ANNALS OF MATHEMATICS, 1993, 137 (02) :295-368
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