About: On symmetries and conservation laws of the Majda-Biello system

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.sciencedirect.com/science/article/pii/S1468121814000996
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. (en)
Title	On symmetries and conservation laws of the Majda-Biello system On symmetries and conservation laws of the Majda-Biello system (en)
skos:prefLabel	On symmetries and conservation laws of the Majda-Biello system On symmetries and conservation laws of the Majda-Biello system (en)
skos:notation	RIV/47813059:19610/15:#0000466!RIV15-MSM-19610___
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(EE2.3.20.0002)
http://linked.open...iv/cisloPeriodika	April 2015
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Vodová, Jiřina
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	329
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/15:#0000466
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Evolution equations; Symmetries; Conservation laws; Hamiltonian operators (en)
http://linked.open.../riv/klicoveSlovo	Evolution equations Conservation laws Hamiltonian operators Symmetries
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[3B3F76EF5EFB]
http://linked.open...i/riv/nazevZdroje	Nonlinear Analysis: Real World Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (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	Vodová-Jahnová, Jiřina
http://linked.open...ain/vavai/riv/wos	000346545700012
issn	1468-1218
number of pages	7 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.nonrwa.2014.08.005
http://localhost/t...ganizacniJednotka	19610

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