Integrability properties of some equations obtained by symmetry reductions
Result 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.
Keywords
Partial differential equationssymmetry reductionssolutionsthe Gibbons-Tsarev equationLax-integrable equations
The result's identifiers
Result code in IS VaVaI
Result on the web
http://www.tandfonline.com/doi/abs/10.1080/14029251.2015.1023582#.VTY2nTe8_AM
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Integrability properties of some equations obtained by symmetry reductions
Original language 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.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
EE2.3.20.0002: Development of Research Capacities of the Mathematical Institute in Opava
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Nonlinear Mathematical Physics
ISSN
1402-9251
e-ISSN
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Volume of the periodical
22
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
23
Pages from-to
210-232
UT code for WoS article
000350561600005
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2015