摘要
本文主要研究在多种形式的耗散前提下一个两维耗散一般化薛定谔方程的扰动平面波解的调制不稳定.我们发现能够出现七族强度递减的平面波解,并且所有的空间依赖指数递减平面波解是线性不稳定的,而所有带有不同耗散的空间独立指数递减平面波解是线性稳定的.特别要说明的是,结果表明五次项比三次项更能使得波传播更稳定.
The modulational instability of perturbed plane-wave solutions of a two-dimensional dissipative generalisation of nonlinear Schr¨odinger（DNLS） equation is investigated in the presence of multiple forms of dissipation. We have found that seven families of decreasing-in-magnitude plane-wave solutions are present and all spatiallydependent exponentially-decaying plane-wave solutions are linearly unstable and all spatially-independent exponentially-decaying plane-wave solutions are linearly stable with different dissipations. Especially, our study shows that the quintic term can make the propagation of waves more stable than the cubic term does.
作者
徐衍聪
乔志琴
陈晓和
XU Yancong;QIAO Zhiqin;CHEN Xiaohe(Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China;School of Science, North University of China, Taiyuan 030051, China)
出处
《应用数学》
CSCD
北大核心
2018年第2期257-268,共12页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(11671114,11401541)
关键词
耗散
非线性薛定谔方程
平面波
调制不稳定
Dissipative
Nonlinear SchrSdinger equation
Plane wave
Modulationalinstability
