Generalized Darboux transformation and localized waves in coupled Hirota equations
Abstract
In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an Nth-order localized wave solution on the plane backgrounds with the same spectral parameter is derived through the direct iterative rule. In particular, some semi-rational, multi-parametric localized wave solutions are obtained: (1) Vector generalization of the first- and the second-order rogue wave solution; (2) Interactional solutions between a dark-bright soliton and a rogue wave, two dark-bright solitons and a second-order rogue wave; (3) Interactional solutions between a breather and a rogue wave, two breathers and a second-order rogue wave. The results further reveal the striking dynamic structures of localized waves in complex coupled systems.
Cite
@article{arxiv.1312.3436,
title = {Generalized Darboux transformation and localized waves in coupled Hirota equations},
author = {Xin Wang and Yuqi Li and Yong Chen},
journal= {arXiv preprint arXiv:1312.3436},
year = {2014}
}