STABILITY OF HASIMOTO SOLITONS IN ENERGY SPACE FOR A FOURTH ORDER NONLINEAR SCHRODINGER TYPE EQUATION

被引：4

作者：

Wang, Zhong ^{[1
]}

机构：

[1] Foshan Univ, Sch Math & Big Data, Foshan 528000, Guangdong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 07期

关键词：

Orbital stability; fourth order; Schrodinger equation; vortex filament; SOLITARY-WAVE SOLUTIONS; VORTEX FILAMENT; ORBITAL STABILITY; STANDING WAVES; MODEL-EQUATIONS; WELL-POSEDNESS; GROUND-STATES; LONG WAVES; POSITIVITY; EXISTENCE;

D O I：

10.3934/dcds.2017174

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we investigate the nonlinear stability of Hasimoto solitons, in energy space, for a fourth order Schrodinger equation (4NLS) which arises in the context of the vortex filament. The proof relies on a suitable Lyapunov functional, at the H-2 level, which allows us to describe the dynamics of small perturbations. This stability result is also extended to Sobolev spaces H-m for all m is an element of Z(+) by employing the infinite conservation laws of 4NLS.

引用

页码：4091 / 4108

页数：18

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