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Statements

Subject Item
n2:RIV%2F47813059%3A19610%2F09%3A%230000273%21RIV10-MSM-19610___
rdf:type
skos:Concept n6:Vysledek
dcterms: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.
dcterms: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
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
skos:notation
RIV/47813059:19610/09:#0000273!RIV10-MSM-19610___
n4:aktivita
n8:Z
n4:aktivity
Z(MSM4781305904)
n4:cisloPeriodika
1-2
n4:dodaniDat
n10:2010
n4:domaciTvurceVysledku
n13:4240650 Błaszak, Maciej
n4:druhVysledku
n12:J
n4:duvernostUdaju
n9:S
n4:entitaPredkladatele
n17:predkladatel
n4:idSjednocenehoVysledku
301221
n4:idVysledku
RIV/47813059:19610/09:#0000273
n4:jazykVysledku
n15:eng
n4:klicovaSlova
L-tensor; Killing tensor; dispersionless integrable systems; reciprocal transformations; weakly nonlinear semi-Hamiltonian hydrodynamic-type systems; generalized hodograph method; conservation laws; Riemann invariants
n4:klicoveSlovo
n7:generalized%20hodograph%20method n7:reciprocal%20transformations n7:weakly%20nonlinear%20semi-Hamiltonian%20hydrodynamic-type%20systems n7:dispersionless%20integrable%20systems n7:Killing%20tensor n7:L-tensor n7:Riemann%20invariants n7:conservation%20laws
n4:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n4:kontrolniKodProRIV
[6CAAC4C83451]
n4:nazevZdroje
Reports on Mathematical Physics
n4:obor
n11:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
2
n4:rokUplatneniVysledku
n10:2009
n4:svazekPeriodika
64
n4:tvurceVysledku
Błaszak, Maciej Sergyeyev, Artur
n4:wos
000271406300023
n4:zamer
n14:MSM4781305904
s:issn
0034-4877
s:numberOfPages
14
n18:organizacniJednotka
19610