Compacton solutions of higher order nonlinear dispersive KdV-like equations

Abstract

In this paper we confirm the existence of compacton solutions that result from genuinely nonlinear dispersive equations. We conduct our study on nonlinear dispersive forms of higher order KdV-like equations. Unlike classical solitons, compacton solutions are non-analytic solutions that generate new form of solitary waves with compact support and with width independent of amplitude. We further show that the defocusing branches of these models generate solitary patterns solutions with infinite slopes or cusps.