Integrability, multiple-cosh , lumps and lump-soliton solutions to a (2+1)-dimensional generalized breaking soliton equation

Abstract

In this paper, we focus on investigating a (2+1)-dimensional generalized breaking soliton (gBS) equation with five model parameters, which contains a lot of important nonlinear partial differential equations (PDEs) as its special cases. Firstly, the integrability features of two special cases of the gBS equation are clarified. Secondly, a general method is established to construct solutions formed by a combination of n−cosh and n−cos expressions. The similar results can be generalized to other PDEs which possess the Hirota bilinear forms. Thirdly, by introducing the nonzero seed solution, we obtain the real non-static lumps, lump-soliton solutions and other relevant exact solutions. The results expand the understanding of lump, freak wave and their interaction solutions in soliton theory. Moreover, various graphical analyses on the presented solutions are made to reveal the dynamic behaviors, which gives an essential improvement in the physical realizing of higher-dimensional lump waves in oceanography and nonlinear optics.