(3+1)-维耦合高阶非线性Schrdinger方程的光学多畸形波

Multi-rogue waves for the(3 + 1)-dimensional coupled higher- order nonlinear Schrdinger equations in optical fiber

本文研究带有高阶项、时间色散项和非线性系数项的复杂(3+1)-维高阶耦合非线性Schrdinger(3DHCNLSE)方程的精确解.首先,利用相似变换将非自治的方程转化为自治的耦合Hirota方程;其次,采用Darboux变换方法得到耦合Hirota方程带有任意常数的有理解;最后,给出变系数3DHCNLSE方程带有任意常数的1阶和2阶多畸形波解.本文获得的(3+1)-维(3D)多畸形波解可以用来描述深海动力学波和非线性光学纤维中出现的一些物理现象.

In this work, we study exact solutions of a （3 ＋ 1）-dimensional higher-order coupled SchrSdinger equation with higher-order terms, the dispersion and the nonlinear coefficients engendering temporal dependency. Similarity transformations are used to convert the nonautonomous equations into autonomous coupled Hirota equations, then we present the multi-rogue wave solutions with arbitrary constants employing the Darboux trans- formations. At last, the first order and second order rogue wave solutions with arbitrary constants are considered for the 3DHCNLSE with variable coefficients by using the similarity transformation and Darboux transformation. The obtained （3 ＋ 1）-dimensional multi-rogue wave solutions can be used to describe the dynamics waves in the deep ocean and nonlinear optical fibers.