A class of localized soliton and fractal pattern solutions of the (2 + 1)-dimensional modified dispersive long wave model

Abstract

The variable separation approach is an important tool to obtain exact localized and fractal structure solutions of higher dimensional nonlinear problems. The general separable solutions involving double random functions are obtained by means of Riccati equation and the variable separation hypothesis. By choosing the suitable arbitrary functions, we obtain a class of localized excitations and fractal structures solutions of the (2 + 1)-dimensional modified dispersive long wave (MDLW) model. Such solutions present couple lump waves, breather wave solutions, dromions, oscillating multi-lumps, oscillating multi-dromoins and ring solitons of the model. Moreover, the fractal lump and fractal dromions type excitation-localized structures of the model are presented here. To visualize the dynamics of each excitation structures are demonstrated by the 3D and density plots.