Darboux transformation of the second-type derivative nonlinear Schr\"odinger equation
Abstract
The second-type derivative nonlinear Schr\"odinger (DNLSII) equation was introduced as an integrable model in 1979. Very recently, the DNLSII equation has been shown by an experiment to be a model of the evolution of optical pulses involving self-steepening without concomitant self-phase-modulation. In this paper the -fold Darboux transformation (DT) of the coupled DNLSII equations is constructed in terms of determinants. Comparing with the usual DT of the soliton equations, this kind of DT is unusual because includes complicated integrals of seed solutions in the process of iteration. By a tedious analysis, these integrals are eliminated in except the integral of the seed solution. Moreover, this is reduced to the DT of the DNLSII equation under a reduction condition. As applications of , the explicit expressions of soliton, rational soliton, breather, rogue wave and multi-rogue wave solutions for the DNLSII equation are displayed.
Keywords
Cite
@article{arxiv.1408.1042,
title = {Darboux transformation of the second-type derivative nonlinear Schr\"odinger equation},
author = {Y. S. Zhang and L. J. Guo and J. S. He and Z. X. Zhou},
journal= {arXiv preprint arXiv:1408.1042},
year = {2015}
}
Comments
The main result of the paper has been presented orally by Yongshuai Zhang at the 12th National Conference on Integrable Systems (Aug.18-22, 2013, Hangzhou, P.R.China). We have submitted it to journal at Sept. 22, 2013. This is the latest version(v29) with 34 pages and 9 figures, which has been accepted by Letters in Mathematical Physics at April 2015