About: A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Using a (1, 1)-tensor L with zero Nijenhuis torsion and maximal possible number (equal to the number of dependent variables) of distinct, functionally independent eigenvalues we define, in a coordinate-free fashion, the seed systems which are weakly nonlinear semi-Hamiltonian systems of a special form, and an infinite set of conservation laws for the seed systems. The reciprocal transformations constructed from these conservation laws yield a considerably larger class of hydrodynamic-type systems from the seed systems, and we show that these new systems are again defined in a coordinate-free manner, using the tensor L alone, and, moreover, are weakly nonlinear and semi-Hamiltonian, so their general solution can be obtained by means of the generalized hodograph method of Tsarev. Using a (1, 1)-tensor L with zero Nijenhuis torsion and maximal possible number (equal to the number of dependent variables) of distinct, functionally independent eigenvalues we define, in a coordinate-free fashion, the seed systems which are weakly nonlinear semi-Hamiltonian systems of a special form, and an infinite set of conservation laws for the seed systems. The reciprocal transformations constructed from these conservation laws yield a considerably larger class of hydrodynamic-type systems from the seed systems, and we show that these new systems are again defined in a coordinate-free manner, using the tensor L alone, and, moreover, are weakly nonlinear and semi-Hamiltonian, so their general solution can be obtained by means of the generalized hodograph method of Tsarev. (en)
Title	A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems (en)
skos:prefLabel	A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems (en)
skos:notation	RIV/47813059:19610/09:#0000273!RIV10-MSM-19610___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	1-2
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Sergyeyev, Artur Błaszak, Maciej
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	301221
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/09:#0000273
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	L-tensor; Killing tensor; dispersionless integrable systems; reciprocal transformations; weakly nonlinear semi-Hamiltonian hydrodynamic-type systems; generalized hodograph method; conservation laws; Riemann invariants (en)
http://linked.open.../riv/klicoveSlovo	conservation laws reciprocal transformations Killing tensor L-tensor generalized hodograph method weakly nonlinear semi-Hamiltonian hydrodynamic-type systems dispersionless integrable systems Riemann invariants
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[6CAAC4C83451]
http://linked.open...i/riv/nazevZdroje	Reports on Mathematical Physics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	64
http://linked.open...iv/tvurceVysledku	Błaszak, Maciej Sergyeyev, Artur
http://linked.open...ain/vavai/riv/wos	000271406300023
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	0034-4877
number of pages	14 (xsd:int)
http://localhost/t...ganizacniJednotka	19610

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