Riemann-Hilbert problem and multiple poles solution for an extended modified Korteweg-de Vries equation with zero/nonzero boundary conditions
The aim is to present the inverse scattering transform (IST) with Riemann-Hilbert problem (RHP) for a higher-order extended modified Korteweg-de Vries (emKdV) equation with zero/nonzero boundary conditions (Z/NZBC) at infinity, where the emKdV equation contains third- and fifth-order dispersion coef...
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| Veröffentlicht in: | Nonlinear dynamics 2022-10, Vol.110 (2), p.1723-1746 |
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| creator | Xiao, Yu Zhu, Qiaozhen Wu, Xing |
| description | The aim is to present the inverse scattering transform (IST) with Riemann-Hilbert problem (RHP) for a higher-order extended modified Korteweg-de Vries (emKdV) equation with zero/nonzero boundary conditions (Z/NZBC) at infinity, where the emKdV equation contains third- and fifth-order dispersion coefficients matching with relevant nonlinearity terms, respectively. Under reflectionless condition, the RHP of emKdV equation is firstly solved when scattering data have two cases: multiple simple poles and higher-order poles, and corresponding formulae of multiple simple poles soliton and higher-order poles solution are shown in terms of determinants, respectively. One simple soliton and two simple soliton solutions are obtained in detail according to variable values of third- and fifth-order dispersion coefficients, the effect power of which are specially displayed in dynamic structures. In addition, as a very important application for solving higher-order solutions by RHP, we extend Laurent’s series of residue conditions of idea to this higher-order emKdV equation. |
| doi_str_mv | 10.1007/s11071-022-07671-5 |
| format | Article |
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Under reflectionless condition, the RHP of emKdV equation is firstly solved when scattering data have two cases: multiple simple poles and higher-order poles, and corresponding formulae of multiple simple poles soliton and higher-order poles solution are shown in terms of determinants, respectively. One simple soliton and two simple soliton solutions are obtained in detail according to variable values of third- and fifth-order dispersion coefficients, the effect power of which are specially displayed in dynamic structures. 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Under reflectionless condition, the RHP of emKdV equation is firstly solved when scattering data have two cases: multiple simple poles and higher-order poles, and corresponding formulae of multiple simple poles soliton and higher-order poles solution are shown in terms of determinants, respectively. One simple soliton and two simple soliton solutions are obtained in detail according to variable values of third- and fifth-order dispersion coefficients, the effect power of which are specially displayed in dynamic structures. In addition, as a very important application for solving higher-order solutions by RHP, we extend Laurent’s series of residue conditions of idea to this higher-order emKdV equation.</description><subject>Automotive Engineering</subject><subject>Boundary conditions</subject><subject>Classical Mechanics</subject><subject>Control</subject><subject>Dispersion</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Inverse scattering</subject><subject>Korteweg-Devries equation</subject><subject>Mechanical Engineering</subject><subject>Original Paper</subject><subject>Poles</subject><subject>Solitary waves</subject><subject>Vibration</subject><issn>0924-090X</issn><issn>1573-269X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kE1LxDAQhoMouK7-AU8Bz9FJ2ibNUcQvFARR8RbSdqqRbrImLX78B_-zWVfw5iUzkOeZSV5C9jkccgB1lDgHxRkIwUDJ3FUbZMYrVTAh9eMmmYEWJQMNj9tkJ6UXACgE1DPydetwYb1nF25oMI50GUMz4IJa39HFNIxuOSBdhgETTWGYRhc87UPM9xTfR_QdZi50rne5uQpxxDd8Yh3Sh-iyg6-T_XHe3PhMPzGGIx_8qtImTL6z8YO2wXduBaVdstXbIeHeb52T-7PTu5MLdn1zfnlyfM3aguuRlbVVspZgoWlKtG1tu77ShWgkguZSS9VIXcq24kr0ZYu8AKtEpfKhhe5FMScH67n5t68TptG8hCn6vNIIJSSvClWrTIk11caQUsTeLKNb5BcbDmYVu1nHbnLs5id2U2WpWEspw_4J49_of6xvQ1WITg</recordid><startdate>20221001</startdate><enddate>20221001</enddate><creator>Xiao, Yu</creator><creator>Zhu, Qiaozhen</creator><creator>Wu, Xing</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0001-6338-4855</orcidid></search><sort><creationdate>20221001</creationdate><title>Riemann-Hilbert problem and multiple poles solution for an extended modified Korteweg-de Vries equation with zero/nonzero boundary conditions</title><author>Xiao, Yu ; Zhu, Qiaozhen ; Wu, Xing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-48a76860a0bb4eac8adf5932b6e0916967b6946c5172f4ce130a7257a72929f23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Automotive Engineering</topic><topic>Boundary conditions</topic><topic>Classical Mechanics</topic><topic>Control</topic><topic>Dispersion</topic><topic>Dynamical Systems</topic><topic>Engineering</topic><topic>Inverse scattering</topic><topic>Korteweg-Devries equation</topic><topic>Mechanical Engineering</topic><topic>Original Paper</topic><topic>Poles</topic><topic>Solitary waves</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xiao, Yu</creatorcontrib><creatorcontrib>Zhu, Qiaozhen</creatorcontrib><creatorcontrib>Wu, Xing</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Nonlinear dynamics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xiao, Yu</au><au>Zhu, Qiaozhen</au><au>Wu, Xing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Riemann-Hilbert problem and multiple poles solution for an extended modified Korteweg-de Vries equation with zero/nonzero boundary conditions</atitle><jtitle>Nonlinear dynamics</jtitle><stitle>Nonlinear Dyn</stitle><date>2022-10-01</date><risdate>2022</risdate><volume>110</volume><issue>2</issue><spage>1723</spage><epage>1746</epage><pages>1723-1746</pages><issn>0924-090X</issn><eissn>1573-269X</eissn><abstract>The aim is to present the inverse scattering transform (IST) with Riemann-Hilbert problem (RHP) for a higher-order extended modified Korteweg-de Vries (emKdV) equation with zero/nonzero boundary conditions (Z/NZBC) at infinity, where the emKdV equation contains third- and fifth-order dispersion coefficients matching with relevant nonlinearity terms, respectively. Under reflectionless condition, the RHP of emKdV equation is firstly solved when scattering data have two cases: multiple simple poles and higher-order poles, and corresponding formulae of multiple simple poles soliton and higher-order poles solution are shown in terms of determinants, respectively. One simple soliton and two simple soliton solutions are obtained in detail according to variable values of third- and fifth-order dispersion coefficients, the effect power of which are specially displayed in dynamic structures. In addition, as a very important application for solving higher-order solutions by RHP, we extend Laurent’s series of residue conditions of idea to this higher-order emKdV equation.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11071-022-07671-5</doi><tpages>24</tpages><orcidid>https://orcid.org/0000-0001-6338-4855</orcidid></addata></record> |
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| subjects | Automotive Engineering Boundary conditions Classical Mechanics Control Dispersion Dynamical Systems Engineering Inverse scattering Korteweg-Devries equation Mechanical Engineering Original Paper Poles Solitary waves Vibration |
| title | Riemann-Hilbert problem and multiple poles solution for an extended modified Korteweg-de Vries equation with zero/nonzero boundary conditions |
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