Multi-soliton, multi-breather and higher order rogue wave solutions to the complex short pulse equation
Multi-soliton, multi-breather and higher order rogue wave solutions to the complex short pulse equation
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复杂短脉冲方程的多孤子、多呼吸和高阶异常波解
DOI：
10.1016/j.physd.2016.03.012
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发表时间：
2016-07-15
影响因子：
4
通讯作者：
Zhu, Zuonong
中科院分区：
文献类型：
--
作者：
Ling, Liming;Feng, Bao-Feng;Zhu, Zuonong
本文研究了复短脉冲（CSP）方程的一般解析解，包括孤子解、呼吸子解和流氓波解。借助于广义达布变换，我们构造了紧行列式形式的N-亮孤子解、包含Akhmediev呼吸子的N-呼吸子解和一般高阶流氓波解.显式给出了一阶和二阶流氓波解，并进行了分析。对N-孤子解和N-呼吸子解进行了严格的渐近分析。所有这三种形式的解析解承认光滑，尖点或循环型的CSP方程取决于参数。值得注意的是，由于互易（速端）变换，CSP方程的流氓波解可以是平滑的、尖点的或循环的，这与迄今为止发现的流氓波解不同。由爱思唯尔公司出版
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.