Group Velocity and Nonlinear Dispersive Wave Propagation
Abstract
By the use of a Hamiltonian formulation, a basic group velocity is defined as the derivative of frequency with respect to wavenumber keeping action density constant, and is shown to represent an incremental action velocity in the general nonlinear case. The stability treatment of Whitham and Lighthill is extended to several dimensions. The waterwave analysis of Whitham (1967a) is extended to two space dimensions, and is shown to predict obliquemode instabilities for kh < 1.36. A treatment of Lighthill's (1965) solution in the onedimensional elliptic case resolves the problem of the energy distribution in the solution past the critical time. A note on diffraction effects on quasilinear solutions of the Whitham type is presented.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 March 1973
 DOI:
 10.1098/rspa.1973.0021
 Bibcode:
 1973RSPSA.332..199H