Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies
The aim of the paper is to construct nonlocal reverse‐space nonlinear Schrödinger (NLS) hierarchies through nonlocal group reductions of eigenvalue problems and generate their inverse scattering transforms and soliton solutions. The inverse scattering problems are formulated by Riemann‐Hilbert probl...
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| Veröffentlicht in: | Studies in applied mathematics (Cambridge) 2020-10, Vol.145 (3), p.563-585 |
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| creator | Ma, Wen‐Xiu Huang, Yehui Wang, Fudong |
| description | The aim of the paper is to construct nonlocal reverse‐space nonlinear Schrödinger (NLS) hierarchies through nonlocal group reductions of eigenvalue problems and generate their inverse scattering transforms and soliton solutions. The inverse scattering problems are formulated by Riemann‐Hilbert problems which determine generalized matrix Jost eigenfunctions. The Sokhotski‐Plemelj formula is used to transform the Riemann‐Hilbert problems into Gelfand‐Levitan‐Marchenko type integral equations. A solution formulation to special Riemann‐Hilbert problems with the identity jump matrix, corresponding to the reflectionless transforms, is presented and applied to N‐soliton solutions of the nonlocal NLS hierarchies. |
| doi_str_mv | 10.1111/sapm.12329 |
| format | Article |
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The inverse scattering problems are formulated by Riemann‐Hilbert problems which determine generalized matrix Jost eigenfunctions. The Sokhotski‐Plemelj formula is used to transform the Riemann‐Hilbert problems into Gelfand‐Levitan‐Marchenko type integral equations. A solution formulation to special Riemann‐Hilbert problems with the identity jump matrix, corresponding to the reflectionless transforms, is presented and applied to N‐soliton solutions of the nonlocal NLS hierarchies.</description><identifier>ISSN: 0022-2526</identifier><identifier>EISSN: 1467-9590</identifier><identifier>DOI: 10.1111/sapm.12329</identifier><language>eng</language><publisher>Cambridge: Blackwell Publishing Ltd</publisher><subject>Eigenvalues ; Eigenvectors ; Hierarchies ; integrable hierarchy ; Integral equations ; Inverse scattering ; matrix eigenvalue problem ; nonlocal reduction ; Riemann‐Hilbert problem ; Solitary waves ; soliton solution ; Transformations (mathematics)</subject><ispartof>Studies in applied mathematics (Cambridge), 2020-10, Vol.145 (3), p.563-585</ispartof><rights>2020 Wiley Periodicals LLC</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3019-6f265a622264d62ec3faaa2fcb701b3f8442921ee8b3005245fb2e1219e6bdbc3</citedby><cites>FETCH-LOGICAL-c3019-6f265a622264d62ec3faaa2fcb701b3f8442921ee8b3005245fb2e1219e6bdbc3</cites><orcidid>0000-0001-5309-1493</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1111%2Fsapm.12329$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1111%2Fsapm.12329$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Ma, Wen‐Xiu</creatorcontrib><creatorcontrib>Huang, Yehui</creatorcontrib><creatorcontrib>Wang, Fudong</creatorcontrib><title>Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies</title><title>Studies in applied mathematics (Cambridge)</title><description>The aim of the paper is to construct nonlocal reverse‐space nonlinear Schrödinger (NLS) hierarchies through nonlocal group reductions of eigenvalue problems and generate their inverse scattering transforms and soliton solutions. The inverse scattering problems are formulated by Riemann‐Hilbert problems which determine generalized matrix Jost eigenfunctions. The Sokhotski‐Plemelj formula is used to transform the Riemann‐Hilbert problems into Gelfand‐Levitan‐Marchenko type integral equations. A solution formulation to special Riemann‐Hilbert problems with the identity jump matrix, corresponding to the reflectionless transforms, is presented and applied to N‐soliton solutions of the nonlocal NLS hierarchies.</description><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Hierarchies</subject><subject>integrable hierarchy</subject><subject>Integral equations</subject><subject>Inverse scattering</subject><subject>matrix eigenvalue problem</subject><subject>nonlocal reduction</subject><subject>Riemann‐Hilbert problem</subject><subject>Solitary waves</subject><subject>soliton solution</subject><subject>Transformations (mathematics)</subject><issn>0022-2526</issn><issn>1467-9590</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1KA0EQhRtRMEY3nqDBnTCxu-YnmWUI_gQiCtF109OpNhMm3WP1RMnOI3gaL-BNPImTjGsLireo772Cx9i5FAPZzlXQ9XogIYb8gPVkkg2jPM3FIesJARBBCtkxOwlhJYSQw1T0GE3dG1JAHoxuGqTSvfCGtAvW0zpw7RY8-KpsvNvppim9C9xb7ryrvNEVJ9z7fz4-Q60N7g-lQ018bpb0_bVoE5H4skTSZFoJp-zI6irg2Z_22fPN9dPkLpo93E4n41lkYiHzKLOQpToDgCxZZIAmtlprsKYYClnEdpQkkINEHBWxECkkqS0AJcgcs2JRmLjPLrrcmvzrBkOjVn5Drn2pIEnSvF0hWuqyowz5EAitqqlca9oqKdSuU7XrVO07bWHZwe9lhdt_SDUfP953nl8bZ335</recordid><startdate>202010</startdate><enddate>202010</enddate><creator>Ma, Wen‐Xiu</creator><creator>Huang, Yehui</creator><creator>Wang, Fudong</creator><general>Blackwell Publishing Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><orcidid>https://orcid.org/0000-0001-5309-1493</orcidid></search><sort><creationdate>202010</creationdate><title>Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies</title><author>Ma, Wen‐Xiu ; Huang, Yehui ; Wang, Fudong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3019-6f265a622264d62ec3faaa2fcb701b3f8442921ee8b3005245fb2e1219e6bdbc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Hierarchies</topic><topic>integrable hierarchy</topic><topic>Integral equations</topic><topic>Inverse scattering</topic><topic>matrix eigenvalue problem</topic><topic>nonlocal reduction</topic><topic>Riemann‐Hilbert problem</topic><topic>Solitary waves</topic><topic>soliton solution</topic><topic>Transformations (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ma, Wen‐Xiu</creatorcontrib><creatorcontrib>Huang, Yehui</creatorcontrib><creatorcontrib>Wang, Fudong</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Studies in applied mathematics (Cambridge)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ma, Wen‐Xiu</au><au>Huang, Yehui</au><au>Wang, Fudong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies</atitle><jtitle>Studies in applied mathematics (Cambridge)</jtitle><date>2020-10</date><risdate>2020</risdate><volume>145</volume><issue>3</issue><spage>563</spage><epage>585</epage><pages>563-585</pages><issn>0022-2526</issn><eissn>1467-9590</eissn><abstract>The aim of the paper is to construct nonlocal reverse‐space nonlinear Schrödinger (NLS) hierarchies through nonlocal group reductions of eigenvalue problems and generate their inverse scattering transforms and soliton solutions. 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| subjects | Eigenvalues Eigenvectors Hierarchies integrable hierarchy Integral equations Inverse scattering matrix eigenvalue problem nonlocal reduction Riemann‐Hilbert problem Solitary waves soliton solution Transformations (mathematics) |
| title | Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies |
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