Soliton perturbation theory for matrix complex modified Korteweg–de Vries equation
In this paper, soliton perturbation theory is extended to an integrable matrix equation. The explicit forms of the eigenstates and eigenvalues related to the linearized differential operator are found and therefore the first correction to the one soliton solution is established. A good agreement bet...
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| Veröffentlicht in: | Wave motion 2018-01, Vol.76, p.42-50 |
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| creator | Ahmadi Zeidabadi, F. Hoseini, S.M. |
| description | In this paper, soliton perturbation theory is extended to an integrable matrix equation. The explicit forms of the eigenstates and eigenvalues related to the linearized differential operator are found and therefore the first correction to the one soliton solution is established. A good agreement between the numerical simulations and analytical results is found.
•Using the AKNS procedure, we determine a matrix version of the complex modified KdV equation.•The problem of the nearly integrable equation is transformed to a linearized differential operator.•We solve the later problem by expanding the solution and the source terms in terms of the eigenfunctions of the linearized operator.•The numerical simulations confirm the analytical results. |
| doi_str_mv | 10.1016/j.wavemoti.2017.09.002 |
| format | Article |
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•Using the AKNS procedure, we determine a matrix version of the complex modified KdV equation.•The problem of the nearly integrable equation is transformed to a linearized differential operator.•We solve the later problem by expanding the solution and the source terms in terms of the eigenfunctions of the linearized operator.•The numerical simulations confirm the analytical results.</description><identifier>ISSN: 0165-2125</identifier><identifier>EISSN: 1878-433X</identifier><identifier>DOI: 10.1016/j.wavemoti.2017.09.002</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Complex modified KdV equation ; Computer simulation ; Continuous and discrete eigenfunctions ; Differential equations ; Eigenvalues ; Integrable matrix equation ; Korteweg-Devries equation ; Numerical analysis ; Perturbation theory ; Soliton perturbation theory ; Studies</subject><ispartof>Wave motion, 2018-01, Vol.76, p.42-50</ispartof><rights>2017</rights><rights>Copyright Elsevier BV Jan 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c340t-da41369a51a13ca42bc7e04a186ee0245704aa7da1566c0649696a9af47dd8e73</citedby><cites>FETCH-LOGICAL-c340t-da41369a51a13ca42bc7e04a186ee0245704aa7da1566c0649696a9af47dd8e73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.wavemoti.2017.09.002$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3541,27915,27916,45986</link.rule.ids></links><search><creatorcontrib>Ahmadi Zeidabadi, F.</creatorcontrib><creatorcontrib>Hoseini, S.M.</creatorcontrib><title>Soliton perturbation theory for matrix complex modified Korteweg–de Vries equation</title><title>Wave motion</title><description>In this paper, soliton perturbation theory is extended to an integrable matrix equation. The explicit forms of the eigenstates and eigenvalues related to the linearized differential operator are found and therefore the first correction to the one soliton solution is established. A good agreement between the numerical simulations and analytical results is found.
•Using the AKNS procedure, we determine a matrix version of the complex modified KdV equation.•The problem of the nearly integrable equation is transformed to a linearized differential operator.•We solve the later problem by expanding the solution and the source terms in terms of the eigenfunctions of the linearized operator.•The numerical simulations confirm the analytical results.</description><subject>Complex modified KdV equation</subject><subject>Computer simulation</subject><subject>Continuous and discrete eigenfunctions</subject><subject>Differential equations</subject><subject>Eigenvalues</subject><subject>Integrable matrix equation</subject><subject>Korteweg-Devries equation</subject><subject>Numerical analysis</subject><subject>Perturbation theory</subject><subject>Soliton perturbation theory</subject><subject>Studies</subject><issn>0165-2125</issn><issn>1878-433X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNqFkM1OwzAQhC0EEqXwCigS54S1kzjxDVTxJypxoCBulmtvwFVTp477d-MdeEOehLSFM6fVSN_MaIeQcwoJBcovJ8lKLbF2wSYMaJGASADYAenRsijjLE3fDkmvA_OYUZYfk5O2nQB0ZCp6ZPTspja4WdSgDws_VsF2Inyg85uocj6qVfB2HWlXN1NcR7UztrJookfnA67w_fvzy2D06i22Ec4XO_8pOarUtMWz39snL7c3o8F9PHy6exhcD2OdZhBiozKacqFyqmiqVcbGukDIFC05IrAsLzqhCqNozrkGngkuuBKqygpjSizSPrnY5zbezRfYBjlxCz_rKiUVAkqWM2AdxfeU9q5tPVay8bZWfiMpyO2CciL_FpTbBSUICTvj1d6I3Q9Li1622uJMo7EedZDG2f8ifgAQ7H-o</recordid><startdate>201801</startdate><enddate>201801</enddate><creator>Ahmadi Zeidabadi, F.</creator><creator>Hoseini, S.M.</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>201801</creationdate><title>Soliton perturbation theory for matrix complex modified Korteweg–de Vries equation</title><author>Ahmadi Zeidabadi, F. ; Hoseini, S.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c340t-da41369a51a13ca42bc7e04a186ee0245704aa7da1566c0649696a9af47dd8e73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Complex modified KdV equation</topic><topic>Computer simulation</topic><topic>Continuous and discrete eigenfunctions</topic><topic>Differential equations</topic><topic>Eigenvalues</topic><topic>Integrable matrix equation</topic><topic>Korteweg-Devries equation</topic><topic>Numerical analysis</topic><topic>Perturbation theory</topic><topic>Soliton perturbation theory</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ahmadi Zeidabadi, F.</creatorcontrib><creatorcontrib>Hoseini, S.M.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Wave motion</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ahmadi Zeidabadi, F.</au><au>Hoseini, S.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Soliton perturbation theory for matrix complex modified Korteweg–de Vries equation</atitle><jtitle>Wave motion</jtitle><date>2018-01</date><risdate>2018</risdate><volume>76</volume><spage>42</spage><epage>50</epage><pages>42-50</pages><issn>0165-2125</issn><eissn>1878-433X</eissn><abstract>In this paper, soliton perturbation theory is extended to an integrable matrix equation. The explicit forms of the eigenstates and eigenvalues related to the linearized differential operator are found and therefore the first correction to the one soliton solution is established. A good agreement between the numerical simulations and analytical results is found.
•Using the AKNS procedure, we determine a matrix version of the complex modified KdV equation.•The problem of the nearly integrable equation is transformed to a linearized differential operator.•We solve the later problem by expanding the solution and the source terms in terms of the eigenfunctions of the linearized operator.•The numerical simulations confirm the analytical results.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.wavemoti.2017.09.002</doi><tpages>9</tpages></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Complex modified KdV equation Computer simulation Continuous and discrete eigenfunctions Differential equations Eigenvalues Integrable matrix equation Korteweg-Devries equation Numerical analysis Perturbation theory Soliton perturbation theory Studies |
| title | Soliton perturbation theory for matrix complex modified Korteweg–de Vries equation |
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