Internal Lagrangians of PDEs as variational principles

A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is est...

Full description

Saved in:
Bibliographic Details
Published in:Journal of geometry and physics 2024-05, Vol.199, p.105143, Article 105143
Main Author: Druzhkov, Kostya
Format: Article
Language:English
Subjects:
Internal Lagrangian
Noether's theorem
Presymplectic structure
Variational principle
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-c307t-524af74aa1574a2064c5b77254e7ee7fc2dde1bfd3707f912fe2a3736dec70a93
container_end_page
container_issue
container_start_page 105143
container_title Journal of geometry and physics
container_volume 199
creator Druzhkov, Kostya
description A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is established. Noether's theorem is formulated in terms of internal Lagrangians. A relation between non-degenerate Lagrangians and the corresponding internal Lagrangians is investigated. Several examples are discussed.
doi_str_mv 10.1016/j.geomphys.2024.105143
format article
fullrecord <record><control><sourceid>elsevier_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1016_j_geomphys_2024_105143</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0393044024000445</els_id><sourcerecordid>S0393044024000445</sourcerecordid><originalsourceid>FETCH-LOGICAL-c307t-524af74aa1574a2064c5b77254e7ee7fc2dde1bfd3707f912fe2a3736dec70a93</originalsourceid><addsrcrecordid>eNqFj91Kw0AQhRdRsFZfQfICibM_2TV3Sq21ENALvV6mm9m6IU3Kbij07U2pXnszA8M5Z87H2D2HggPXD22xpWG3_z6mQoBQ07HkSl6wGX80Vc61FpdsBrKSOSgF1-wmpRYAtKr4jOl1P1Lssctq3EbstwH7lA0--3hZpgxTdsAYcAzDSbKPoXdh31G6ZVceu0R3v3vOvl6Xn4u3vH5frRfPde4kmDEvhUJvFCIvpymmn67cGCNKRYbIeCeahvjGN9KA8RUXngRKI3VDzgBWcs70OdfFIaVI3k4ddhiPloM90dvW_tHbE70900_Gp7ORpnaHQNEmF6h31IRIbrTNEP6L-AF-1Wbf</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Internal Lagrangians of PDEs as variational principles</title><source>ScienceDirect Freedom Collection</source><source>Backfile Package - Physics General (Legacy) [YPA]</source><creator>Druzhkov, Kostya</creator><creatorcontrib>Druzhkov, Kostya</creatorcontrib><description>A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is established. Noether's theorem is formulated in terms of internal Lagrangians. A relation between non-degenerate Lagrangians and the corresponding internal Lagrangians is investigated. Several examples are discussed.</description><identifier>ISSN: 0393-0440</identifier><identifier>EISSN: 1879-1662</identifier><identifier>DOI: 10.1016/j.geomphys.2024.105143</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Internal Lagrangian ; Noether's theorem ; Presymplectic structure ; Variational principle</subject><ispartof>Journal of geometry and physics, 2024-05, Vol.199, p.105143, Article 105143</ispartof><rights>2024 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c307t-524af74aa1574a2064c5b77254e7ee7fc2dde1bfd3707f912fe2a3736dec70a93</cites><orcidid>0000-0003-3190-6465</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0393044024000445$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3632,27924,27925,46012</link.rule.ids></links><search><creatorcontrib>Druzhkov, Kostya</creatorcontrib><title>Internal Lagrangians of PDEs as variational principles</title><title>Journal of geometry and physics</title><description>A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is established. Noether's theorem is formulated in terms of internal Lagrangians. A relation between non-degenerate Lagrangians and the corresponding internal Lagrangians is investigated. Several examples are discussed.</description><subject>Internal Lagrangian</subject><subject>Noether's theorem</subject><subject>Presymplectic structure</subject><subject>Variational principle</subject><issn>0393-0440</issn><issn>1879-1662</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNqFj91Kw0AQhRdRsFZfQfICibM_2TV3Sq21ENALvV6mm9m6IU3Kbij07U2pXnszA8M5Z87H2D2HggPXD22xpWG3_z6mQoBQ07HkSl6wGX80Vc61FpdsBrKSOSgF1-wmpRYAtKr4jOl1P1Lssctq3EbstwH7lA0--3hZpgxTdsAYcAzDSbKPoXdh31G6ZVceu0R3v3vOvl6Xn4u3vH5frRfPde4kmDEvhUJvFCIvpymmn67cGCNKRYbIeCeahvjGN9KA8RUXngRKI3VDzgBWcs70OdfFIaVI3k4ddhiPloM90dvW_tHbE70900_Gp7ORpnaHQNEmF6h31IRIbrTNEP6L-AF-1Wbf</recordid><startdate>202405</startdate><enddate>202405</enddate><creator>Druzhkov, Kostya</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-3190-6465</orcidid></search><sort><creationdate>202405</creationdate><title>Internal Lagrangians of PDEs as variational principles</title><author>Druzhkov, Kostya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c307t-524af74aa1574a2064c5b77254e7ee7fc2dde1bfd3707f912fe2a3736dec70a93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Internal Lagrangian</topic><topic>Noether's theorem</topic><topic>Presymplectic structure</topic><topic>Variational principle</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Druzhkov, Kostya</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of geometry and physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Druzhkov, Kostya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Internal Lagrangians of PDEs as variational principles</atitle><jtitle>Journal of geometry and physics</jtitle><date>2024-05</date><risdate>2024</risdate><volume>199</volume><spage>105143</spage><pages>105143-</pages><artnum>105143</artnum><issn>0393-0440</issn><eissn>1879-1662</eissn><abstract>A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is established. Noether's theorem is formulated in terms of internal Lagrangians. A relation between non-degenerate Lagrangians and the corresponding internal Lagrangians is investigated. Several examples are discussed.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.geomphys.2024.105143</doi><orcidid>https://orcid.org/0000-0003-3190-6465</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0393-0440
ispartof Journal of geometry and physics, 2024-05, Vol.199, p.105143, Article 105143
issn 0393-0440
1879-1662
language eng
recordid cdi_crossref_primary_10_1016_j_geomphys_2024_105143
source ScienceDirect Freedom Collection; Backfile Package - Physics General (Legacy) [YPA]
subjects Internal Lagrangian
Noether's theorem
Presymplectic structure
Variational principle
title Internal Lagrangians of PDEs as variational principles
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T17%3A55%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-elsevier_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Internal%20Lagrangians%20of%20PDEs%20as%20variational%20principles&rft.jtitle=Journal%20of%20geometry%20and%20physics&rft.au=Druzhkov,%20Kostya&rft.date=2024-05&rft.volume=199&rft.spage=105143&rft.pages=105143-&rft.artnum=105143&rft.issn=0393-0440&rft.eissn=1879-1662&rft_id=info:doi/10.1016/j.geomphys.2024.105143&rft_dat=%3Celsevier_cross%3ES0393044024000445%3C/elsevier_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c307t-524af74aa1574a2064c5b77254e7ee7fc2dde1bfd3707f912fe2a3736dec70a93%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true