Ermakov-modulated nonlinear schrödinger models. integrable reduction

Abstract

Nonlinear Schrodinger equations with spatial modulation associated with integrable Hamiltonian systems of Ermakov-Ray-Reid type are introduced. An algorithmic procedure is presented which exploits invariants of motion to construct exact wave packet representations with potential applications in a wide range of physical contexts such as, 'inter alia', the analysis of Bloch wave and matter wave solitonic propagation and pulse transmission in Airy modulated NLS models. A particular Ermakov reduction for Mooney-Rivlin materials is set in the broader context of transverse wave propagation in a class of higher-order hyperelastic models of incompressible solids.