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 Schroedinger 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.
Carroll-type deformations in nonlinear elastodynamics
SACCOMANDI, Giuseppe;Vergori, Luigi
2014
Abstract
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 Schroedinger 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
