On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation

A vector modified Yajima−Oikawa long-wave−short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and generalized Darboux transformations for...

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Main Authors:	Xianguo Geng, Ruomeng Li
Format:	Article
Language:	English
Published:	MDPI AG 2019-10-01
Series:	Mathematics
Subjects:	vector modified long-wave–short-wave equation multi-fold generalized darboux transformation soliton solutions breather solutions rogue wave solutions
Online Access:	https://www.mdpi.com/2227-7390/7/10/958

id	doaj-270c8cec04df4f65b38d8986d85ba95e
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spelling	doaj-270c8cec04df4f65b38d8986d85ba95e2020-11-25T02:03:41ZengMDPI AGMathematics2227-73902019-10-0171095810.3390/math7100958math7100958On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave EquationXianguo Geng0Ruomeng Li1School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, ChinaSchool of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, ChinaA vector modified Yajima−Oikawa long-wave−short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and generalized Darboux transformations for the vector modified Yajima−Oikawa long-wave−short-wave equation. As applications of the multi-fold classical Darboux transformations and generalized Darboux transformations, various exact solutions for the vector modified long-wave−short-wave equation are obtained, including soliton, breather, and rogue wave solutions.https://www.mdpi.com/2227-7390/7/10/958vector modified long-wave–short-wave equationmulti-fold generalized darboux transformationsoliton solutionsbreather solutionsrogue wave solutions
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xianguo Geng Ruomeng Li
spellingShingle	Xianguo Geng Ruomeng Li On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation Mathematics vector modified long-wave–short-wave equation multi-fold generalized darboux transformation soliton solutions breather solutions rogue wave solutions
author_facet	Xianguo Geng Ruomeng Li
author_sort	Xianguo Geng
title	On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation
title_short	On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation
title_full	On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation
title_fullStr	On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation
title_full_unstemmed	On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation
title_sort	on a vector modified yajima–oikawa long-wave–short-wave equation
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-10-01
description	A vector modified Yajima−Oikawa long-wave−short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and generalized Darboux transformations for the vector modified Yajima−Oikawa long-wave−short-wave equation. As applications of the multi-fold classical Darboux transformations and generalized Darboux transformations, various exact solutions for the vector modified long-wave−short-wave equation are obtained, including soliton, breather, and rogue wave solutions.
topic	vector modified long-wave–short-wave equation multi-fold generalized darboux transformation soliton solutions breather solutions rogue wave solutions
url	https://www.mdpi.com/2227-7390/7/10/958
work_keys_str_mv	AT xianguogeng onavectormodifiedyajimaoikawalongwaveshortwaveequation AT ruomengli onavectormodifiedyajimaoikawalongwaveshortwaveequation
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On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation

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