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Group classification and conservation laws of anisotropic wave equations with a source
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
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2016 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 57, no 8, 083504Article in journal (Refereed) Published
Abstract [en]

Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2016. Vol. 57, no 8, 083504
National Category
Other Mathematics
URN: urn:nbn:se:bth-12978DOI: 10.1063/1.4960800ISI: 000383917300054ScopusID: 2-s2.0-84982311630OAI: diva2:956868
Available from: 2016-08-31 Created: 2016-08-31 Last updated: 2016-11-01Bibliographically approved

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Ibragimov, Nail
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