Two classes of fractal structures for the (2+1)-dimensional dispersive long wave equation

Abstract

Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW) equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.