Breather, soliton molecules, soliton fusions and fissions, and lump wave of the Caudrey-Dodd-Gibbon equation

Abstract

In this article, our attention is focused on the exploration of new features of the Caudrey-Dodd-Gibbon (CDG) equation arising from fluid mechanism. We introduce a constant in the transformation, which links the solution and auxiliary function defined in the bilinear form. By constructing different auxiliary function, we calculate the breather solution, one- to three-soliton solutions and lump wave solution. We report that a breather can be generated from a stripe-like soliton. We discover the soliton molecules and their interaction where the maximum amplitude will decrease as they overlap. Two types of heterotypic solitons, namely, soliton fusions and fissions are obtained by attaining their constrain conditions, respectively. We also observe this equation possesses several unique features, such as, having only the two-soliton molecules but not N (N ≥ 3)-soliton molecules, and having the line-like lump wave parallel to the x-axis but not to the t-axis.