Localized wave solutions for (2+1)-dimensional third-order Fokou-Kofane-Mohamadou-Yomba equation

Abstract Analytical and numerical investigations of localized wave solutions for a nonlinear evolution of shallow water waves with surface tension, which is described by the (2+1)-dimensional third-order Fokou-Kofane-Mohamadou-Yomba (FKMY) equation are performed. Furthermore, we show, mainly by Maple software and the Hirota bilinear method, that appropriated ansatzes can be used to generate new large families of traveling localized structures such as lump, soliton, periodic soliton, quasi-periodic soliton, and quasi-periodic breather solutions. Interactions between those soliton solutions and their dependence on the system physical parameters have been carefully analysed. We show that the soliton solutions of the 2D third-order FKMY display a very rich spectrum of dynamical behaviour when its parameters are varied. The present results could be applicable in explaining the basic features of localized disturbances in many fields of science where the 2D third-order FKMY equation appears.