Multi-soliton, multi-breather and higher order rogue wave solutions to the complex short pulse equation

PHYSICA D-NONLINEAR PHENOMENA

卷:327

Article

Ling, Liming¹  Feng, Bao-Feng²  Zhu, Zuonong³ 

[1] S China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

[2] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

[3] Shanghai Jiao Tong Univ, Dept Math, Shanghai, Peoples R China

关键词: Complex short pulse equation;    Darboux transformation;    Bright soliton;    Breather soliton;    Rogue wave;    Asymptotic analysis;   

DOI  :  10.1016/j.physd.2016.03.012

来源: Elsevier

【 摘 要 】

In the present paper, we are concerned with the general analytic solutions to the complex short pulse (CSP) equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the N-bright soliton solution in a compact determinant form, the N-breather solution including the Akhmediev breather and a general higher order rogue wave solution. The first and second order rogue wave solutions are given explicitly and analyzed. The asymptotic analysis is performed rigorously for both the N-soliton and the N-breather solutions. All three forms of the analytical solutions admit either smoothed-, cusped- or looped-type ones for the CSP equation depending on the parameters. It is noted that, due to the reciprocal (hodograph) transformation, the rogue wave solution to the CSP equation can be a smoothed, cusponed or a looped one, which is different from the rogue wave solution found so far. Published by Elsevier B.V.

【 授权许可】

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