Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions

2011/08/31 by Boling Guo, Liming Ling, Q. P. Liu · 2 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1103/physreve.85.026607

published as Physical Review E 85 (2012) 026607 · 17 pages, 4 figures, replaced by revised version

arxiv created 2011/11/22 · arxiv updated 2015/05/29

Abstract

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

Cited by

• Exploration of Higher-order Nondegenerate Soliton solutions for Manakov model via Gram-determinant Darboux transformation
• Rogue-wave and lump patterns associated with the third Painlevé equation

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• Generalized Darboux transformation and higher-order rogue wave solutions to the Manakov system
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