Carroll-type deformations in nonlinear elastodynamics

Classes of deformations in nonlinear elastodynamics with origins in the pioneering work of Carroll are investigated for a Mooney-Rivlin material subject to body forces corresponding to a nonlinear substrate potential. Exact representations are obtained which, inter alia, are descriptive of the propa...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 47; no. 20; pp. 205204 - 17
Main Authors Rogers, C, Saccomandi, G, Vergori, L
Format Journal Article
LanguageEnglish
Published IOP Publishing 23.05.2014
Subjects
Deformation
Elastodynamics
exact solutions
Klein-Gordon equation
Mathematical analysis
nonlinear elasticity
nonlinear Schrödinger equations
Nonlinearity
Origins
Representations
Schroedinger equation
Wave propagation
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Summary:Classes of deformations in nonlinear elastodynamics with origins in the pioneering work of Carroll are investigated for a Mooney-Rivlin material subject to body forces corresponding to a nonlinear substrate potential. Exact representations are obtained which, inter alia, are descriptive of the propagation of circularly polarized waves and motions with oscillatory spatial dependence. It is shown that a description of slowly modulated waves leads to a novel class of generalized nonlinear Schrödinger equations. The latter class, in general, is not integrable. However, a procedure is presented whereby integrable Hamiltonian subsystems may be isolated for a broad class of deformations.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/20/205204