Nonlinear elastodynamics of materials with strong ellipticity condition: Carroll-type solutions

• Published in: Wave motion Vol. 56; pp. 147 - 164
• Main Authors: Rogers, C., Saccomandi, G., Vergori, L.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2015
• Subjects: Compact waves; Deformation; Elastic deformation; Elastodynamics; Exact solutions; Mathematical analysis; Nonlinear Klein–Gordon equation; Nonlinear Schrödinger equation; Nonlinearity; Schroedinger equation; Wave propagation; Nonlinear Klein–Gordon equation; Compact waves; Nonlinear Schrödinger equation
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2015.02.009

Classes of deformations in nonlinear elastodynamics with origin in pioneering work of Carroll are investigated for an isotropic elastic solid subject to body forces corresponding to a nonlinear substrate potential. Exact solutions are obtained which, inter alia, are descriptive of the propagation of compact 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. •Nonlinear Klein–Gordon equation in nonlinear elastodynamics: compact-like waves and waves with oscillatory spatial dependence.•Derivation of the nonlinear Schrödinger (NLS) equation from the nonlinear Klein–Gordon equation.•Modulated NLS-type equation: compactons and standing waves.