About: Integrability properties of some equations obtained by symmetry reductions

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.tandfonline.com/doi/abs/10.1080/14029251.2015.1023582#.VTY2nTe8_AM
Description	In our recent paper [1], we gave a complete description of symmetry reduction of four Lax-integrable (i.e., possessing a zero-curvature representation with a non-removable parameter) 3-dimensional equations. Here we study the behavior of the integrability features of the initial equations under the reduction procedure. We show that the ZCRs are transformed to nonlinear differential coverings of the resulting 2D-systems similar to the one found for the Gibbons-Tsarev equation in [17]. Using these coverings we construct infinite series of (nonlocal) conservation laws and prove their nontriviality. We also show that the recursion operators are not preserved under reductions. In our recent paper [1], we gave a complete description of symmetry reduction of four Lax-integrable (i.e., possessing a zero-curvature representation with a non-removable parameter) 3-dimensional equations. Here we study the behavior of the integrability features of the initial equations under the reduction procedure. We show that the ZCRs are transformed to nonlinear differential coverings of the resulting 2D-systems similar to the one found for the Gibbons-Tsarev equation in [17]. Using these coverings we construct infinite series of (nonlocal) conservation laws and prove their nontriviality. We also show that the recursion operators are not preserved under reductions. (en)
Title	Integrability properties of some equations obtained by symmetry reductions Integrability properties of some equations obtained by symmetry reductions (en)
skos:prefLabel	Integrability properties of some equations obtained by symmetry reductions Integrability properties of some equations obtained by symmetry reductions (en)
skos:notation	RIV/47813059:19610/15:#0000469!RIV15-MSM-19610___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(EE2.3.20.0002)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Baran, Hynek Vojčák, Petr Krasil'shchik, Iosif S.
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	215
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/15:#0000469
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Partial differential equations; symmetry reductions; solutions; the Gibbons-Tsarev equation; Lax-integrable equations (en)
http://linked.open.../riv/klicoveSlovo	Partial differential equations Lax-integrable equations the Gibbons-Tsarev equation solutions symmetry reductions
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[880D6D75BD99]
http://linked.open...i/riv/nazevZdroje	Journal of Nonlinear Mathematical Physics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Development of Research Capacities of the Mathematical Institute in Opava
http://linked.open...UplatneniVysledku	2015
http://linked.open...v/svazekPeriodika	22
http://linked.open...iv/tvurceVysledku	Vojčák, Petr Baran, Hynek Morozov, Oleg I. Krasil'shchik, Iosif S.
http://linked.open...ain/vavai/riv/wos	000350561600005
issn	1402-9251
number of pages	23 (xsd:int)
http://bibframe.org/vocab/doi	10.1080/14029251.2015.1023582
http://localhost/t...ganizacniJednotka	19610

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