On the integrability of a class of nonlinear dispersive wave equations

Abstract

We investigate the integrability of a class of 1+1 dimensional models describing non-linear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations. © 2005 Taylor & Francis Group, LLC.