No abstract

In this paper, the Hirota’s bilinear form is employed to investigate the lump, periodic lump and interaction lump stripe solutions of the (2+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation. Many results are obtained by dynamic process of figures. We analyze the propagation direction and horizontal velocity of lump solutions to find some constraint conditions which include positiveness and localization. In the process of the travel of the periodic lump solutions, it appears that the energy distribution is not symmetrical. The interaction lump stripe solutions of non-elastic indicate that the lump solitons are dropped and swallowed by the stripe soliton.

No abstract

The Broer-Kaup equation is one of many equations describing some phenomena of shallow water wave. There are many errors in scientific research because of the existence of the non-smooth boundaries. In this paper, we generalize the Broer-Kaup equation to the fractal space and establish fractal variational formulations through the semi-inverse method. The acquired fractal variational formulation reveals conservation laws in an energy form in the fractal space and suggests possible solution structures of the morphology of the solitary waves.

In this paper, associating with the Hirota bilinear form, the three-wave method, which is applied to construct some periodic wave solutions of (3+1)-dimensional soliton equation, is a powerful approach to obtain periodic solutions for many non-linear evolution equations in the integrable systems theory.