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Statements

Subject Item
n2:RIV%2F47813059%3A19610%2F15%3A%230000466%21RIV15-MSM-19610___
rdf:type
skos:Concept n20:Vysledek
rdfs:seeAlso
http://www.sciencedirect.com/science/article/pii/S1468121814000996
dcterms:description
In 2003, A.J. Majda and J.A. Biello derived and studied the so-called reduced equations for equatorial baroclinic-barotropic waves, to which we refer as to the Majda-Biello system. The equations in question describe the nonlinear interaction of long-wavelength equatorial Rossby waves and barotropic Rossby waves with a significant midlatitude projection in the presence of suitable horizontally and vertically sheared zonal mean flows. Below we present a Hamiltonian structure for Majda-Biello system and describe all generalized symmetries and conservation laws for the latter. It turns out that there are only three symmetries corresponding to x-translations, t-translations and to a scaling of t, x, u and v, and four conservation laws, one of which is associated with the conservation of energy, the second conserved quantity is just the Hamiltonian functional and the other two are Casimir functionals of the Hamiltonian operator admitted by our system. Our result provides inter alia a rigorous proof of the fact that the Majda-Biello system has just the conservation laws mentioned in the paper by Majda and Biello. In 2003, A.J. Majda and J.A. Biello derived and studied the so-called reduced equations for equatorial baroclinic-barotropic waves, to which we refer as to the Majda-Biello system. The equations in question describe the nonlinear interaction of long-wavelength equatorial Rossby waves and barotropic Rossby waves with a significant midlatitude projection in the presence of suitable horizontally and vertically sheared zonal mean flows. Below we present a Hamiltonian structure for Majda-Biello system and describe all generalized symmetries and conservation laws for the latter. It turns out that there are only three symmetries corresponding to x-translations, t-translations and to a scaling of t, x, u and v, and four conservation laws, one of which is associated with the conservation of energy, the second conserved quantity is just the Hamiltonian functional and the other two are Casimir functionals of the Hamiltonian operator admitted by our system. Our result provides inter alia a rigorous proof of the fact that the Majda-Biello system has just the conservation laws mentioned in the paper by Majda and Biello.
dcterms:title
On symmetries and conservation laws of the Majda-Biello system On symmetries and conservation laws of the Majda-Biello system
skos:prefLabel
On symmetries and conservation laws of the Majda-Biello system On symmetries and conservation laws of the Majda-Biello system
skos:notation
RIV/47813059:19610/15:#0000466!RIV15-MSM-19610___
n4:aktivita
n12:I n12:P
n4:aktivity
I, P(EE2.3.20.0002)
n4:cisloPeriodika
April 2015
n4:dodaniDat
n15:2015
n4:domaciTvurceVysledku
n7:8967245
n4:druhVysledku
n11:J
n4:duvernostUdaju
n17:S
n4:entitaPredkladatele
n9:predkladatel
n4:idSjednocenehoVysledku
329
n4:idVysledku
RIV/47813059:19610/15:#0000466
n4:jazykVysledku
n5:eng
n4:klicovaSlova
Evolution equations; Symmetries; Conservation laws; Hamiltonian operators
n4:klicoveSlovo
n8:Symmetries n8:Conservation%20laws n8:Hamiltonian%20operators n8:Evolution%20equations
n4:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n4:kontrolniKodProRIV
[3B3F76EF5EFB]
n4:nazevZdroje
Nonlinear Analysis: Real World Applications
n4:obor
n19:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
1
n4:projekt
n14:EE2.3.20.0002
n4:rokUplatneniVysledku
n15:2015
n4:svazekPeriodika
22
n4:tvurceVysledku
Vodová-Jahnová, Jiřina
n4:wos
000346545700012
s:issn
1468-1218
s:numberOfPages
7
n13:doi
10.1016/j.nonrwa.2014.08.005
n18:organizacniJednotka
19610