Nonlinear Schrodinger equation: Generalized Darboux transformation and rogue wave solutions

被引：855

作者：

Guo, Boling ^{[1
]}

Ling, Liming ^{[1
]}

Liu, Q. P. ^{[2
]}

机构：

[1] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China

[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China

来源：

PHYSICAL REVIEW E | 2012年 / 85卷 / 02期

基金：

中国国家自然科学基金;

关键词：

NLS EQUATION; POSITONS; SOLITONS;

D O I：

10.1103/PhysRevE.85.026607

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

In this paper, we construct a generalized Darboux transformation for the nonlinear Schrodinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrodinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.

引用

页数：9

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