用Hirota双线性导数变换求MNLS方程的Rogue波解

The Rogue Wave Solution of MNLS Equation Based on Hirota’s Bi-linear Derivative Transformation

修正的非线性薛定谔方程(MNLS方程)与导数非线性薛定谔方程(DNLS方程)是两个紧密相关且完全可积的非线性偏微分方程.该文通过Hirota双线性导数变换方法,首先求得MNLS方程在平面简谐波背景下的空间周期解,即Akhmediev型呼吸子解,再通过长波极限得其Rogue波解.根据简单的参数归零法使之自然地约化为DNLS方程的Rogue波解,并借助于一个积分变换将其变换为Chen-Lee-Liu方程的Rogue波解.文章还简要讨论了MNLS方程和DNLS方程在非局域情形整体解的存在性问题.

The modified nonlinear Schrodinger(MNLS for brevity)equation and the Derivative nonlinear Schrodinger(DNLS for brevity)equation are two nonlinear differential equations that are closely correlated and fully integrable.Firstly,the spatially periodic breather solution of the MNLS equation has been obtained by method of Hirota’s bilinear derivative transform,and then its rogue wave solution is also obtained by a long-wave limit of the Akhmediev-type breather,which can be naturally reduced to a rogue wave solution of the DNLS equation by a simple operation of parameters.The existence of global soliton/rogue wave solutions for the MNLS/DNLS equations is briefly discussed.