Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations
type: Item
instance of: scholarly article
title: Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations
zbMATH Open document ID: 1361.35160
author: Chong Liu
author: Xin Wang
author: Lei Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-02-08T00:00:00Z
review text: A Lax pair is a pair of linear operators, which is associated with a given partial differential equation. It is usually quite difficult to find the Lax pair corresponding to a given PDE. Therefore, often first the Lax pair is defined, and then the corresponding PDE is computed. For the Hirota equations in this article, possibly no Lax pair is known. The authors have a coupled Hirota equation (CH) and want to express this by using a DT (Darboux transformation). The CH system in [\textit{S. Chen} and \textit{L.-Yan Song}, ``Rogue waves in coupled Hirota systems'', Phys. Rev. E 87, No. 3 (2013; \url{doi:10.1103/physreve.87.032910})] is not the same as the one in equations 1 and 2 (which are not proved). The proofs use the AKNS technique and DT in explicit matrix form. Rough waves with multiple compression points are illustrated by pictures. Several abbreviations, which are used in the text are presented in the introduction.
reviewed by: Thomas Ernst
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 6682109
zbMATH Keywords: integrable system
zbMATH Keywords: Darboux transformation
zbMATH Keywords: rogue wave
zbMATH Keywords: variable-coefficients coupled Hirota equations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2016.12.079
OpenAlex ID: W2571506496
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DOI: 10.1016/J.JMAA.2016.12.079
description: scientific article; zbMATH DE number 6682109