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Bifurcation of Nonlinear Conservation Laws from the Classical Energy Conservation Law for Internal Gravity Waves in Cylindrical Wave Field
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
2013 (English)In: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, Vol. 8, no 5, 119-130 p.Article in journal (Refereed) Published
Abstract [en]

New conservation laws bifurcating from the classical form of conservation laws are constructed to the nonlinear Boussinesq model describing internal Kelvin waves propagating in a cylindrical wave field of an uniformly stratified water affected by the earth's rotation. The obtained conservation laws are different from the well known energy conservation law for internal waves and they are associated with symmetries of the Boussinesq model. Particularly, it is shown that application of Lie group analysis provide three infinite sets of nontrivial integral conservation laws depending on two arbitrary functions, namely a(t, theta),b(t, r) and an arbitrary function c(t, theta, r) which is given implicitly as a nontrivial solution of a partial differential equation involving a(t, theta) and b(t,r).

Place, publisher, year, edition, pages
EDP Sciences , 2013. Vol. 8, no 5, 119-130 p.
Keyword [en]
Kelvin internal waves, conservation laws
National Category
URN: urn:nbn:se:bth-6855DOI: 10.1051/mmnp/20138508ISI: 000325837500008Local ID: diva2:834406
Available from: 2013-11-25 Created: 2013-11-25 Last updated: 2015-06-30Bibliographically approved

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Ibragimov, Nail
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Department of Mathematics and Natural Sciences
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