Neumann Type Integrable Reduction to the Negative-Order Coupled Harry–Dym Hierarchy

Based on the Lax compatibility, the negative-order coupled Harry–Dym (ncHD) hierarchy depending upon one parameter α is retrieved in the Lenard scheme, which includes the two-component Camassa–Holm (2CH) equation as a special member with α=−1/4. By using a symmetric constraint, it is found that only...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of the Physical Society of Japan 2018-10, Vol.87 (10), p.104004
1. Verfasser: Chen, Jinbing
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 10
container_start_page 104004
container_title Journal of the Physical Society of Japan
container_volume 87
creator Chen, Jinbing
description Based on the Lax compatibility, the negative-order coupled Harry–Dym (ncHD) hierarchy depending upon one parameter α is retrieved in the Lenard scheme, which includes the two-component Camassa–Holm (2CH) equation as a special member with α=−1/4. By using a symmetric constraint, it is found that only in the case of α > 1 the ncHD hierarchy can be reduced to a family of backward Neumann type systems by separating the temporal and spatial variables on the tangent bundle of a unit sphere. The resultant backward Neumann type systems are proved to be completely integrable in the Liouville sense via a Lax equation. Finally, for α > 1, the relation between the ncHD hierarchy and the backward Neumann type systems is established, where the involutive solutions of backward Neumann type systems yield the finite parametric solutions to the ncHD hierarchy.
doi_str_mv 10.7566/JPSJ.87.104004
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2111121825</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2111121825</sourcerecordid><originalsourceid>FETCH-LOGICAL-c294t-1f05d37bf87419c93999e2d0a701fb7f436308f7b73dd8b5a44affd84c07e5f13</originalsourceid><addsrcrecordid>eNotkL1OwzAUhS0EEqWwMltiTriO7ToZUflpq6pF0M6WE1-3qdokOA5SNt6BN-RJKCpnOcunc6SPkFsGsZKj0f3s9X0WpypmIADEGRkwLlQkQPFzMgDgLMqAyUty1bY7gESyRAzIeoHdwVQVXfUN0mkVcONNvkf6hrYrQllXNNQ0bJEucGNC-YnR0lv0dFx3zR4tnRjv-5-v78f-QCcleuOLbX9NLpzZt3jz30Oyfn5ajSfRfPkyHT_MoyLJRIiYA2m5yl2qBMuKjGdZhokFo4C5XDnBRxxSp3LFrU1zaYQwztlUFKBQOsaH5O602_j6o8M26F3d-ep4qRN2TMLSRB6p-EQVvm5bj043vjwY32sG-k-d_lOnU6VP6vgv-7Vh_g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2111121825</pqid></control><display><type>article</type><title>Neumann Type Integrable Reduction to the Negative-Order Coupled Harry–Dym Hierarchy</title><source>Alma/SFX Local Collection</source><creator>Chen, Jinbing</creator><creatorcontrib>Chen, Jinbing</creatorcontrib><description>Based on the Lax compatibility, the negative-order coupled Harry–Dym (ncHD) hierarchy depending upon one parameter α is retrieved in the Lenard scheme, which includes the two-component Camassa–Holm (2CH) equation as a special member with α=−1/4. By using a symmetric constraint, it is found that only in the case of α &gt; 1 the ncHD hierarchy can be reduced to a family of backward Neumann type systems by separating the temporal and spatial variables on the tangent bundle of a unit sphere. The resultant backward Neumann type systems are proved to be completely integrable in the Liouville sense via a Lax equation. Finally, for α &gt; 1, the relation between the ncHD hierarchy and the backward Neumann type systems is established, where the involutive solutions of backward Neumann type systems yield the finite parametric solutions to the ncHD hierarchy.</description><identifier>ISSN: 0031-9015</identifier><identifier>EISSN: 1347-4073</identifier><identifier>DOI: 10.7566/JPSJ.87.104004</identifier><language>eng</language><publisher>Tokyo: The Physical Society of Japan</publisher><subject>Hierarchies ; Integral equations ; Mathematical functions ; Partial differential equations</subject><ispartof>Journal of the Physical Society of Japan, 2018-10, Vol.87 (10), p.104004</ispartof><rights>Copyright The Physical Society of Japan Oct 15, 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c294t-1f05d37bf87419c93999e2d0a701fb7f436308f7b73dd8b5a44affd84c07e5f13</citedby><cites>FETCH-LOGICAL-c294t-1f05d37bf87419c93999e2d0a701fb7f436308f7b73dd8b5a44affd84c07e5f13</cites><orcidid>0000-0002-5250-509X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Chen, Jinbing</creatorcontrib><title>Neumann Type Integrable Reduction to the Negative-Order Coupled Harry–Dym Hierarchy</title><title>Journal of the Physical Society of Japan</title><description>Based on the Lax compatibility, the negative-order coupled Harry–Dym (ncHD) hierarchy depending upon one parameter α is retrieved in the Lenard scheme, which includes the two-component Camassa–Holm (2CH) equation as a special member with α=−1/4. By using a symmetric constraint, it is found that only in the case of α &gt; 1 the ncHD hierarchy can be reduced to a family of backward Neumann type systems by separating the temporal and spatial variables on the tangent bundle of a unit sphere. The resultant backward Neumann type systems are proved to be completely integrable in the Liouville sense via a Lax equation. Finally, for α &gt; 1, the relation between the ncHD hierarchy and the backward Neumann type systems is established, where the involutive solutions of backward Neumann type systems yield the finite parametric solutions to the ncHD hierarchy.</description><subject>Hierarchies</subject><subject>Integral equations</subject><subject>Mathematical functions</subject><subject>Partial differential equations</subject><issn>0031-9015</issn><issn>1347-4073</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNotkL1OwzAUhS0EEqWwMltiTriO7ToZUflpq6pF0M6WE1-3qdokOA5SNt6BN-RJKCpnOcunc6SPkFsGsZKj0f3s9X0WpypmIADEGRkwLlQkQPFzMgDgLMqAyUty1bY7gESyRAzIeoHdwVQVXfUN0mkVcONNvkf6hrYrQllXNNQ0bJEucGNC-YnR0lv0dFx3zR4tnRjv-5-v78f-QCcleuOLbX9NLpzZt3jz30Oyfn5ajSfRfPkyHT_MoyLJRIiYA2m5yl2qBMuKjGdZhokFo4C5XDnBRxxSp3LFrU1zaYQwztlUFKBQOsaH5O602_j6o8M26F3d-ep4qRN2TMLSRB6p-EQVvm5bj043vjwY32sG-k-d_lOnU6VP6vgv-7Vh_g</recordid><startdate>20181015</startdate><enddate>20181015</enddate><creator>Chen, Jinbing</creator><general>The Physical Society of Japan</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-5250-509X</orcidid></search><sort><creationdate>20181015</creationdate><title>Neumann Type Integrable Reduction to the Negative-Order Coupled Harry–Dym Hierarchy</title><author>Chen, Jinbing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c294t-1f05d37bf87419c93999e2d0a701fb7f436308f7b73dd8b5a44affd84c07e5f13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Hierarchies</topic><topic>Integral equations</topic><topic>Mathematical functions</topic><topic>Partial differential equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Jinbing</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of the Physical Society of Japan</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Jinbing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Neumann Type Integrable Reduction to the Negative-Order Coupled Harry–Dym Hierarchy</atitle><jtitle>Journal of the Physical Society of Japan</jtitle><date>2018-10-15</date><risdate>2018</risdate><volume>87</volume><issue>10</issue><spage>104004</spage><pages>104004-</pages><issn>0031-9015</issn><eissn>1347-4073</eissn><abstract>Based on the Lax compatibility, the negative-order coupled Harry–Dym (ncHD) hierarchy depending upon one parameter α is retrieved in the Lenard scheme, which includes the two-component Camassa–Holm (2CH) equation as a special member with α=−1/4. By using a symmetric constraint, it is found that only in the case of α &gt; 1 the ncHD hierarchy can be reduced to a family of backward Neumann type systems by separating the temporal and spatial variables on the tangent bundle of a unit sphere. The resultant backward Neumann type systems are proved to be completely integrable in the Liouville sense via a Lax equation. Finally, for α &gt; 1, the relation between the ncHD hierarchy and the backward Neumann type systems is established, where the involutive solutions of backward Neumann type systems yield the finite parametric solutions to the ncHD hierarchy.</abstract><cop>Tokyo</cop><pub>The Physical Society of Japan</pub><doi>10.7566/JPSJ.87.104004</doi><orcidid>https://orcid.org/0000-0002-5250-509X</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0031-9015
ispartof Journal of the Physical Society of Japan, 2018-10, Vol.87 (10), p.104004
issn 0031-9015
1347-4073
language eng
recordid cdi_proquest_journals_2111121825
source Alma/SFX Local Collection
subjects Hierarchies
Integral equations
Mathematical functions
Partial differential equations
title Neumann Type Integrable Reduction to the Negative-Order Coupled Harry–Dym Hierarchy
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T23%3A26%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Neumann%20Type%20Integrable%20Reduction%20to%20the%20Negative-Order%20Coupled%20Harry%E2%80%93Dym%20Hierarchy&rft.jtitle=Journal%20of%20the%20Physical%20Society%20of%20Japan&rft.au=Chen,%20Jinbing&rft.date=2018-10-15&rft.volume=87&rft.issue=10&rft.spage=104004&rft.pages=104004-&rft.issn=0031-9015&rft.eissn=1347-4073&rft_id=info:doi/10.7566/JPSJ.87.104004&rft_dat=%3Cproquest_cross%3E2111121825%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2111121825&rft_id=info:pmid/&rfr_iscdi=true