Algebraic and geometric structures of analytic partial differential equations

Algebraic and geometric structures of analytic partial differential equations

We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinit...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Theoretical and mathematical physics 2016-11, Vol.189 (2), p.1592-1608
1. Verfasser: Kaptsov, O. V.
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Mathematical and Computational Physics
Nonlinear differential equations
Physics
Physics and Astronomy
Theoretical
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1608
container_issue 2
container_start_page 1592
container_title Theoretical and mathematical physics
container_volume 189
creator Kaptsov, O. V.
description We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.
doi_str_mv 10.1134/S0040577916110052
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1880824503</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1880824503</sourcerecordid><originalsourceid>FETCH-LOGICAL-c311t-4459aed80ba5ccda6f5b934a2232db63be25852adb68165baa5457cc21db21ff3</originalsourceid><addsrcrecordid>eNp1UD1PwzAQtRBIlMIPYIvEHPD5I3HGqgKKVMQAzNHZsatUadLaztB_j0sYkBDT3bv3odMj5BboPQAXD--UCirLsoICgFLJzsgMZMnzinN-TmYnOj_xl-QqhC2lSaRgRl4X3cZqj63JsG-yjR12NvqEQvSjiaO3IRtc4rA7xnTeo48tdlnTOme97b-BPYwY26EP1-TCYRfszc-ck8-nx4_lKl-_Pb8sF-vccICYCyErtI2iGqUxDRZO6ooLZIyzRhdcWyaVZJh2BYXUiFLI0hgGjWbgHJ-Tuyl374fDaEOst8Po04-hBqWoYkJSnlQwqYwfQvDW1Xvf7tAfa6D1qbX6T2vJwyZPSNp-Y_2v5H9NX0L0bzc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1880824503</pqid></control><display><type>article</type><title>Algebraic and geometric structures of analytic partial differential equations</title><source>Springer Nature - Complete Springer Journals</source><creator>Kaptsov, O. V.</creator><creatorcontrib>Kaptsov, O. V.</creatorcontrib><description>We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.</description><identifier>ISSN: 0040-5779</identifier><identifier>EISSN: 1573-9333</identifier><identifier>DOI: 10.1134/S0040577916110052</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Applications of Mathematics ; Mathematical and Computational Physics ; Nonlinear differential equations ; Physics ; Physics and Astronomy ; Theoretical</subject><ispartof>Theoretical and mathematical physics, 2016-11, Vol.189 (2), p.1592-1608</ispartof><rights>Pleiades Publishing, Ltd. 2016</rights><rights>Copyright Springer Science &amp; Business Media 2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c311t-4459aed80ba5ccda6f5b934a2232db63be25852adb68165baa5457cc21db21ff3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0040577916110052$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0040577916110052$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Kaptsov, O. V.</creatorcontrib><title>Algebraic and geometric structures of analytic partial differential equations</title><title>Theoretical and mathematical physics</title><addtitle>Theor Math Phys</addtitle><description>We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.</description><subject>Applications of Mathematics</subject><subject>Mathematical and Computational Physics</subject><subject>Nonlinear differential equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Theoretical</subject><issn>0040-5779</issn><issn>1573-9333</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1UD1PwzAQtRBIlMIPYIvEHPD5I3HGqgKKVMQAzNHZsatUadLaztB_j0sYkBDT3bv3odMj5BboPQAXD--UCirLsoICgFLJzsgMZMnzinN-TmYnOj_xl-QqhC2lSaRgRl4X3cZqj63JsG-yjR12NvqEQvSjiaO3IRtc4rA7xnTeo48tdlnTOme97b-BPYwY26EP1-TCYRfszc-ck8-nx4_lKl-_Pb8sF-vccICYCyErtI2iGqUxDRZO6ooLZIyzRhdcWyaVZJh2BYXUiFLI0hgGjWbgHJ-Tuyl374fDaEOst8Po04-hBqWoYkJSnlQwqYwfQvDW1Xvf7tAfa6D1qbX6T2vJwyZPSNp-Y_2v5H9NX0L0bzc</recordid><startdate>20161101</startdate><enddate>20161101</enddate><creator>Kaptsov, O. V.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20161101</creationdate><title>Algebraic and geometric structures of analytic partial differential equations</title><author>Kaptsov, O. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c311t-4459aed80ba5ccda6f5b934a2232db63be25852adb68165baa5457cc21db21ff3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Applications of Mathematics</topic><topic>Mathematical and Computational Physics</topic><topic>Nonlinear differential equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kaptsov, O. V.</creatorcontrib><collection>CrossRef</collection><jtitle>Theoretical and mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kaptsov, O. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Algebraic and geometric structures of analytic partial differential equations</atitle><jtitle>Theoretical and mathematical physics</jtitle><stitle>Theor Math Phys</stitle><date>2016-11-01</date><risdate>2016</risdate><volume>189</volume><issue>2</issue><spage>1592</spage><epage>1608</epage><pages>1592-1608</pages><issn>0040-5779</issn><eissn>1573-9333</eissn><abstract>We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0040577916110052</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0040-5779
ispartof Theoretical and mathematical physics, 2016-11, Vol.189 (2), p.1592-1608
issn 0040-5779
1573-9333
language eng
recordid cdi_proquest_journals_1880824503
source Springer Nature - Complete Springer Journals
subjects Applications of Mathematics
Mathematical and Computational Physics
Nonlinear differential equations
Physics
Physics and Astronomy
Theoretical
title Algebraic and geometric structures of analytic partial differential equations
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T06%3A24%3A07IST&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=Algebraic%20and%20geometric%20structures%20of%20analytic%20partial%20differential%20equations&rft.jtitle=Theoretical%20and%20mathematical%20physics&rft.au=Kaptsov,%20O.%20V.&rft.date=2016-11-01&rft.volume=189&rft.issue=2&rft.spage=1592&rft.epage=1608&rft.pages=1592-1608&rft.issn=0040-5779&rft.eissn=1573-9333&rft_id=info:doi/10.1134/S0040577916110052&rft_dat=%3Cproquest_cross%3E1880824503%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=1880824503&rft_id=info:pmid/&rfr_iscdi=true