Nonlinear Schr\"odinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
Exactly Solvable and Integrable Systems
2015-05-30 v2
Abstract
In this paper, we construct a generalized Darboux transformation for nonlinear Schr\"odinger equation. The associated -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 -th order rogue wave solutions of the focusing nonlinear Schr\"odinger equation and Hirota equation. In particular, the dynamics of the general third order rogue wave is discussed and shown to exhibit interesting structure.
Cite
@article{arxiv.1108.2867,
title = {Nonlinear Schr\"odinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions},
author = {Boling Guo and Liming Ling and Q. P. Liu},
journal= {arXiv preprint arXiv:1108.2867},
year = {2015}
}
Comments
17 pages, 4 figures, replaced by revised version