A Five-Component Generalized mKdV Equation and Its Exact Solutions

A Five-Component Generalized mKdV Equation and Its Exact Solutions

In this paper, a <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula> spectral problem is proposed and a five-component...

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Main Authors: Bo Xue, Huiling Du, Ruomeng Li
Format: Article
Language:English
Published: MDPI AG 2020-07-01
Series:Mathematics
Subjects:
gauge transformation
Darboux transformation
explicit solution
Online Access:https://www.mdpi.com/2227-7390/8/7/1145
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spelling doaj-b3beac51871d40cb8f353925a1efbff02020-11-25T02:33:57ZengMDPI AGMathematics2227-73902020-07-0181145114510.3390/math8071145A Five-Component Generalized mKdV Equation and Its Exact SolutionsBo Xue0Huiling Du1Ruomeng Li2School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou 450001, ChinaSchool of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou 450001, ChinaSchool of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou 450001, ChinaIn this paper, a <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula> spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations between the Lax pairs. As applications of the Darboux transformations, interesting exact solutions, including soliton-like solutions and a solution that consists of rational functions of <inline-formula> <math display="inline"> <semantics> <msup> <mi>e</mi> <mi>x</mi> </msup> </semantics> </math> </inline-formula> and <i>t</i>, for the five-component equation are obtained.https://www.mdpi.com/2227-7390/8/7/1145gauge transformationDarboux transformationexplicit solution
collection DOAJ
language English
format Article
sources DOAJ
author Bo Xue
Huiling Du
Ruomeng Li
spellingShingle Bo Xue
Huiling Du
Ruomeng Li
A Five-Component Generalized mKdV Equation and Its Exact Solutions
Mathematics
gauge transformation
Darboux transformation
explicit solution
author_facet Bo Xue
Huiling Du
Ruomeng Li
author_sort Bo Xue
title A Five-Component Generalized mKdV Equation and Its Exact Solutions
title_short A Five-Component Generalized mKdV Equation and Its Exact Solutions
title_full A Five-Component Generalized mKdV Equation and Its Exact Solutions
title_fullStr A Five-Component Generalized mKdV Equation and Its Exact Solutions
title_full_unstemmed A Five-Component Generalized mKdV Equation and Its Exact Solutions
title_sort five-component generalized mkdv equation and its exact solutions
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-07-01
description In this paper, a <inline-formula> <math display="inline"> <semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula> spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations between the Lax pairs. As applications of the Darboux transformations, interesting exact solutions, including soliton-like solutions and a solution that consists of rational functions of <inline-formula> <math display="inline"> <semantics> <msup> <mi>e</mi> <mi>x</mi> </msup> </semantics> </math> </inline-formula> and <i>t</i>, for the five-component equation are obtained.
topic gauge transformation
Darboux transformation
explicit solution
url https://www.mdpi.com/2227-7390/8/7/1145
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AT huilingdu afivecomponentgeneralizedmkdvequationanditsexactsolutions
AT ruomengli afivecomponentgeneralizedmkdvequationanditsexactsolutions
AT boxue fivecomponentgeneralizedmkdvequationanditsexactsolutions
AT huilingdu fivecomponentgeneralizedmkdvequationanditsexactsolutions
AT ruomengli fivecomponentgeneralizedmkdvequationanditsexactsolutions
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