A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation

In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. By means of the Euler–Lagrange equations, a suitable Jacobi–Ostrogradsky coordinate system is established. Using Cao’s method and the associated...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2023-11, Vol.11 (21), p.4539
Main Authors: Liu, Wei, Liu, Yafeng, Wei, Junxuan, Yuan, Shujuan
Format: Article
Language:English
Subjects:
Coordinates
Differential equations
Eigenvalues
Euler-Lagrange equation
involutive solution
Kadometsev–Petviashvili equation
Mathematical analysis
Mathematical functions
Nonlinear equations
nonlinearization of Lax pairs
Partial differential equations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c326t-c57da0725cd90df0a2257fa844e881f832de61d9c11cfda54473e9f4114241df3
container_end_page
container_issue 21
container_start_page 4539
container_title Mathematics (Basel)
container_volume 11
creator Liu, Wei
Liu, Yafeng
Wei, Junxuan
Yuan, Shujuan
description In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. By means of the Euler–Lagrange equations, a suitable Jacobi–Ostrogradsky coordinate system is established. Using Cao’s method and the associated Bargmann constraint, the Lax pairs of the differential equations are nonlinearized. Then, a new kind of finite-dimensional Hamilton system is generated. Moreover, involutive representations of the solutions of the Kadometsev–Petviashvili equation are derived.
doi_str_mv 10.3390/math11214539
format article
fullrecord <record><control><sourceid>gale_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_fca5747f03a14a3babf8096ca706bd9d</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A772534945</galeid><doaj_id>oai_doaj_org_article_fca5747f03a14a3babf8096ca706bd9d</doaj_id><sourcerecordid>A772534945</sourcerecordid><originalsourceid>FETCH-LOGICAL-c326t-c57da0725cd90df0a2257fa844e881f832de61d9c11cfda54473e9f4114241df3</originalsourceid><addsrcrecordid>eNpNkdtqGzEQhkVJocHNXR5gobfdVKe1Vpcmh9YkkNID5E6MpZEts7tKJNmQu7xD3zBPErUOJdKFhn9mPkbzE3LK6JkQmn4ZoWwY40x2Qr8jx5xz1aqaOHoTfyAnOW9pPZqJXupjcrdorsIUCrYXYcQphzjB0CyngusEqwGbn4-54Nj8wAEKuqbEpmywuQYXRywZ989Pf75j2QfIm30YQnP5sINSKR_Jew9DxpPXd0Z-X13-Ov_W3tx-XZ4vblor-Ly0tlMOqOKddZo6T4HzTnnopcS-Z74X3OGcOW0Zs95BJ6USqL1kTHLJnBczsjxwXYStuU9hhPRoIgTzT4hpbSCVYAc03kKnpPJUAJMgVrDyPdVzC4rOV067yvp0YN2n-LDDXMw27lJdSDa87-ssXGtdq84OVWuo0DD5WBLYeh2OwcYJfaj6QtVPCamrHTPy-dBgU8w5of8_JqPmr3fmrXfiBfkljTg</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2888322999</pqid></control><display><type>article</type><title>A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation</title><source>Publicly Available Content Database</source><creator>Liu, Wei ; Liu, Yafeng ; Wei, Junxuan ; Yuan, Shujuan</creator><creatorcontrib>Liu, Wei ; Liu, Yafeng ; Wei, Junxuan ; Yuan, Shujuan</creatorcontrib><description>In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. By means of the Euler–Lagrange equations, a suitable Jacobi–Ostrogradsky coordinate system is established. Using Cao’s method and the associated Bargmann constraint, the Lax pairs of the differential equations are nonlinearized. Then, a new kind of finite-dimensional Hamilton system is generated. Moreover, involutive representations of the solutions of the Kadometsev–Petviashvili equation are derived.</description><identifier>ISSN: 2227-7390</identifier><identifier>EISSN: 2227-7390</identifier><identifier>DOI: 10.3390/math11214539</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Coordinates ; Differential equations ; Eigenvalues ; Euler-Lagrange equation ; involutive solution ; Kadometsev–Petviashvili equation ; Mathematical analysis ; Mathematical functions ; Nonlinear equations ; nonlinearization of Lax pairs ; Partial differential equations</subject><ispartof>Mathematics (Basel), 2023-11, Vol.11 (21), p.4539</ispartof><rights>COPYRIGHT 2023 MDPI AG</rights><rights>2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c326t-c57da0725cd90df0a2257fa844e881f832de61d9c11cfda54473e9f4114241df3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2888322999/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2888322999?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25752,27923,27924,37011,44589,74997</link.rule.ids></links><search><creatorcontrib>Liu, Wei</creatorcontrib><creatorcontrib>Liu, Yafeng</creatorcontrib><creatorcontrib>Wei, Junxuan</creatorcontrib><creatorcontrib>Yuan, Shujuan</creatorcontrib><title>A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation</title><title>Mathematics (Basel)</title><description>In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. By means of the Euler–Lagrange equations, a suitable Jacobi–Ostrogradsky coordinate system is established. Using Cao’s method and the associated Bargmann constraint, the Lax pairs of the differential equations are nonlinearized. Then, a new kind of finite-dimensional Hamilton system is generated. Moreover, involutive representations of the solutions of the Kadometsev–Petviashvili equation are derived.</description><subject>Coordinates</subject><subject>Differential equations</subject><subject>Eigenvalues</subject><subject>Euler-Lagrange equation</subject><subject>involutive solution</subject><subject>Kadometsev–Petviashvili equation</subject><subject>Mathematical analysis</subject><subject>Mathematical functions</subject><subject>Nonlinear equations</subject><subject>nonlinearization of Lax pairs</subject><subject>Partial differential equations</subject><issn>2227-7390</issn><issn>2227-7390</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNpNkdtqGzEQhkVJocHNXR5gobfdVKe1Vpcmh9YkkNID5E6MpZEts7tKJNmQu7xD3zBPErUOJdKFhn9mPkbzE3LK6JkQmn4ZoWwY40x2Qr8jx5xz1aqaOHoTfyAnOW9pPZqJXupjcrdorsIUCrYXYcQphzjB0CyngusEqwGbn4-54Nj8wAEKuqbEpmywuQYXRywZ989Pf75j2QfIm30YQnP5sINSKR_Jew9DxpPXd0Z-X13-Ov_W3tx-XZ4vblor-Ly0tlMOqOKddZo6T4HzTnnopcS-Z74X3OGcOW0Zs95BJ6USqL1kTHLJnBczsjxwXYStuU9hhPRoIgTzT4hpbSCVYAc03kKnpPJUAJMgVrDyPdVzC4rOV067yvp0YN2n-LDDXMw27lJdSDa87-ssXGtdq84OVWuo0DD5WBLYeh2OwcYJfaj6QtVPCamrHTPy-dBgU8w5of8_JqPmr3fmrXfiBfkljTg</recordid><startdate>20231101</startdate><enddate>20231101</enddate><creator>Liu, Wei</creator><creator>Liu, Yafeng</creator><creator>Wei, Junxuan</creator><creator>Yuan, Shujuan</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>DOA</scope></search><sort><creationdate>20231101</creationdate><title>A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation</title><author>Liu, Wei ; Liu, Yafeng ; Wei, Junxuan ; Yuan, Shujuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-c57da0725cd90df0a2257fa844e881f832de61d9c11cfda54473e9f4114241df3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Coordinates</topic><topic>Differential equations</topic><topic>Eigenvalues</topic><topic>Euler-Lagrange equation</topic><topic>involutive solution</topic><topic>Kadometsev–Petviashvili equation</topic><topic>Mathematical analysis</topic><topic>Mathematical functions</topic><topic>Nonlinear equations</topic><topic>nonlinearization of Lax pairs</topic><topic>Partial differential equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Wei</creatorcontrib><creatorcontrib>Liu, Yafeng</creatorcontrib><creatorcontrib>Wei, Junxuan</creatorcontrib><creatorcontrib>Yuan, Shujuan</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content 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><collection>ProQuest Central Basic</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Mathematics (Basel)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Wei</au><au>Liu, Yafeng</au><au>Wei, Junxuan</au><au>Yuan, Shujuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation</atitle><jtitle>Mathematics (Basel)</jtitle><date>2023-11-01</date><risdate>2023</risdate><volume>11</volume><issue>21</issue><spage>4539</spage><pages>4539-</pages><issn>2227-7390</issn><eissn>2227-7390</eissn><abstract>In this paper, the Kadometsev–Petviashvili equation and the Bargmann system are obtained from a second-order operator spectral problem Lφ=(∂2−v∂−λu)φ=λφx. By means of the Euler–Lagrange equations, a suitable Jacobi–Ostrogradsky coordinate system is established. Using Cao’s method and the associated Bargmann constraint, the Lax pairs of the differential equations are nonlinearized. Then, a new kind of finite-dimensional Hamilton system is generated. Moreover, involutive representations of the solutions of the Kadometsev–Petviashvili equation are derived.</abstract><cop>Basel</cop><pub>MDPI AG</pub><doi>10.3390/math11214539</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2227-7390
ispartof Mathematics (Basel), 2023-11, Vol.11 (21), p.4539
issn 2227-7390
2227-7390
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_fca5747f03a14a3babf8096ca706bd9d
source Publicly Available Content Database
subjects Coordinates
Differential equations
Eigenvalues
Euler-Lagrange equation
involutive solution
Kadometsev–Petviashvili equation
Mathematical analysis
Mathematical functions
Nonlinear equations
nonlinearization of Lax pairs
Partial differential equations
title A Finite-Dimensional Integrable System Related to the Kadometsev–Petviashvili Equation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T06%3A35%3A58IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Finite-Dimensional%20Integrable%20System%20Related%20to%20the%20Kadometsev%E2%80%93Petviashvili%20Equation&rft.jtitle=Mathematics%20(Basel)&rft.au=Liu,%20Wei&rft.date=2023-11-01&rft.volume=11&rft.issue=21&rft.spage=4539&rft.pages=4539-&rft.issn=2227-7390&rft.eissn=2227-7390&rft_id=info:doi/10.3390/math11214539&rft_dat=%3Cgale_doaj_%3EA772534945%3C/gale_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c326t-c57da0725cd90df0a2257fa844e881f832de61d9c11cfda54473e9f4114241df3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2888322999&rft_id=info:pmid/&rft_galeid=A772534945&rfr_iscdi=true