Conservation Laws and Symmetries of Semilinear Radial Wave Equations

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dc.creatorAnco, Stephen C.
dc.creatorIvanova, Nataliya M.
dc.date2006-08-15
dc.date2006-11-15
dc.date.accessioned2026-07-07T07:59:22Z
dc.date.available2026-07-07T07:59:22Z
dc.descriptionClassifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger equation and its derivative variant, and two proposed radial generalizations of modified Korteweg--de Vries equations, as well as Hamiltonian variants. The mains results classify all admitted local point symmetries and all admitted local conserved densities depending on up to first order spatial derivatives, including any that exist only for special powers or dimensions. All such cases for which these wave equations admit, in particular, dilational energies or conformal energies and inversion symmetries are determined. In addition, potential systems arising from the classified conservation laws are used to determine nonlocal symmetries and nonlocal conserved quantities admitted by these equations. As illustrative applications, a discussion is given of energy norms, conserved H^s norms, critical powers for blow-up solutions, and one-dimensional optimal symmetry groups for invariant solutions.
dc.description16 pages. Final version with minor revisions
dc.identifierhttps://arxiv.org/abs/math-ph/0608037
dc.identifierhttp://arxiv.org/abs/math-ph/0608037
dc.identifierJ. Math. Anal. Appl. 332 (2006), 863-876.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128341
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject70S10; 35L65; 37K05; 35Q53; 35Q55
dc.titleConservation Laws and Symmetries of Semilinear Radial Wave Equations
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