Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions

✍ Scribed by Guo, Boling; Ling, Liming; Liu, Q. P.

• Book ID: 118148562
• Publisher: The American Physical Society
• Year: 2012
• Tongue: English
• Weight: 332 KB
• Volume: 85
• Category: Article
• ISSN: 1063-651X
• DOI: 10.1103/physreve.85.026607

✦ Synopsis

In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger 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 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 structures.