Nonlinear waves in the modulation instability regime for the fifth-order nonlinear Schrodinger equation

被引：31

作者：

Li, Ping ^{[1
]}

Wang, Lei ^{[1
]}

Kong, Liang-Qian ^{[1
]}

Wang, Xin ^{[2
]}

Xie, Ze-Yu ^{[3
]}

机构：

[1] North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China

[2] Zhongyuan Univ Technol, Coll Sci, Zhengzhou 450007, Henan, Peoples R China

[3] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2018年 / 85卷

基金：

中国国家自然科学基金;

关键词：

Higher-order effects; Modulation instability; Nonlinear waves; Numerical simulation; Perturbation energy;

D O I：

10.1016/j.aml.2018.05.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the linear stability analysis and nonlinear excitations on a continuous wave background for the fifth-order nonlinear Schrodinger equation. We find that there are a modulation stability (MS) quasi-elliptic ring and a MS curve in the modulation instability (MI) regime. The concrete expressions of different types of nonlinear waves are obtained by using Darboux transformation. And we present the relations and phase diagram between MI and these waves. We discover that the antidark (AD) soliton and nonrational W-shaped soliton can only exist on the resonance line of outside of the MS quasi-elliptic ring and the right of the MS curve. We perform numerical simulation to test the stability of the AD soliton. By introducing the perturbation energy, we further show that solitons in the MI regime are caused by both the fourth- and fifth-order effects. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：110 / 117

页数：8

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