Quasi-Noether Systems and Quasi-Lagrangians

We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same conservation laws as Lagrange (Green−Lagrange) identity. We d...
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Autor*in:	V. Rosenhaus [verfasserIn] Ravi Shankar [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	symmetries conservation laws Noether operator identity quasi-Noether systems quasi-Lagrangians

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 11(2019), 8, p 1008
Übergeordnetes Werk:	volume:11 ; year:2019 ; number:8, p 1008

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym11081008

Katalog-ID:	DOAJ085306967

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520			\|a We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same conservation laws as Lagrange (Green−Lagrange) identity. We discuss quasi-Noether systems, and some of their properties, and generate classes of quasi-Noether differential equations of the second order. We next introduce a more general version of quasi-Lagrangians which allows us to extend Noether theorem. Here, variational symmetries are only sub-symmetries, not true symmetries. We finally introduce the critical point condition for evolution equations with a conserved integral, demonstrate examples of its compatibility, and compare the invariant submanifolds of quasi-Lagrangian systems with those of Hamiltonian systems.
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language	English
source	In Symmetry 11(2019), 8, p 1008 volume:11 year:2019 number:8, p 1008
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topic_facet	symmetries conservation laws Noether operator identity quasi-Noether systems quasi-Lagrangians Mathematics
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callnumber-first	Q - Science
author	V. Rosenhaus
spellingShingle	V. Rosenhaus misc QA1-939 misc symmetries misc conservation laws misc Noether operator identity misc quasi-Noether systems misc quasi-Lagrangians misc Mathematics Quasi-Noether Systems and Quasi-Lagrangians
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topic_title	QA1-939 Quasi-Noether Systems and Quasi-Lagrangians symmetries conservation laws Noether operator identity quasi-Noether systems quasi-Lagrangians
topic	misc QA1-939 misc symmetries misc conservation laws misc Noether operator identity misc quasi-Noether systems misc quasi-Lagrangians misc Mathematics
topic_unstemmed	misc QA1-939 misc symmetries misc conservation laws misc Noether operator identity misc quasi-Noether systems misc quasi-Lagrangians misc Mathematics
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title	Quasi-Noether Systems and Quasi-Lagrangians
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title_auth	Quasi-Noether Systems and Quasi-Lagrangians
abstract	We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same conservation laws as Lagrange (Green−Lagrange) identity. We discuss quasi-Noether systems, and some of their properties, and generate classes of quasi-Noether differential equations of the second order. We next introduce a more general version of quasi-Lagrangians which allows us to extend Noether theorem. Here, variational symmetries are only sub-symmetries, not true symmetries. We finally introduce the critical point condition for evolution equations with a conserved integral, demonstrate examples of its compatibility, and compare the invariant submanifolds of quasi-Lagrangian systems with those of Hamiltonian systems.
abstractGer	We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same conservation laws as Lagrange (Green−Lagrange) identity. We discuss quasi-Noether systems, and some of their properties, and generate classes of quasi-Noether differential equations of the second order. We next introduce a more general version of quasi-Lagrangians which allows us to extend Noether theorem. Here, variational symmetries are only sub-symmetries, not true symmetries. We finally introduce the critical point condition for evolution equations with a conserved integral, demonstrate examples of its compatibility, and compare the invariant submanifolds of quasi-Lagrangian systems with those of Hamiltonian systems.
abstract_unstemmed	We study differential systems for which it is possible to establish a correspondence between symmetries and conservation laws based on Noether identity: quasi-Noether systems. We analyze Noether identity and show that it leads to the same conservation laws as Lagrange (Green−Lagrange) identity. We discuss quasi-Noether systems, and some of their properties, and generate classes of quasi-Noether differential equations of the second order. We next introduce a more general version of quasi-Lagrangians which allows us to extend Noether theorem. Here, variational symmetries are only sub-symmetries, not true symmetries. We finally introduce the critical point condition for evolution equations with a conserved integral, demonstrate examples of its compatibility, and compare the invariant submanifolds of quasi-Lagrangian systems with those of Hamiltonian systems.
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Quasi-Noether Systems and Quasi-Lagrangians

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