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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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/7/1145 |
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| author | Bo Xue Huiling Du Ruomeng Li |
| author_facet | Bo Xue Huiling Du Ruomeng Li |
| author_sort | Bo Xue |
| collection | DOAJ |
| 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. |
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| format | Article |
| id | doaj.art-b3beac51871d40cb8f353925a1efbff0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:30:52Z |
| publishDate | 2020-07-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b3beac51871d40cb8f353925a1efbff02023-11-20T06:37:51ZengMDPI AGMathematics2227-73902020-07-0187114510.3390/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 |
| spellingShingle | Bo Xue Huiling Du Ruomeng Li A Five-Component Generalized mKdV Equation and Its Exact Solutions Mathematics gauge transformation Darboux transformation explicit solution |
| title | 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_short | A Five-Component Generalized mKdV Equation and Its Exact Solutions |
| title_sort | five component generalized mkdv equation and its exact solutions |
| topic | gauge transformation Darboux transformation explicit solution |
| url | https://www.mdpi.com/2227-7390/8/7/1145 |
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