Lump, periodic lump and interaction lump stripe solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

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.

A fractal variational theory of the Broer-Kaup system in shallow water waves

“…In view of Eqs. (2.13) and (2.14), ( , ) F u v can be written as 4 2 . Fv =− (21) Finally, we successfully establish the variational formulation…”

“…Recently, many methods have been used to study shallow water waves [1][2]. The Broer-Kaup equation (BK equation), as a model describing the bi-directional propagation of the long waves, plays an important role in the study of shallow water wave.…”

Variational theory for a kind of non-linear model for water waves

“…Nowadays, the study of shallow water waves is a very hot topic [1][2][3][4]. This paper, we mainly focus on the Whitham-Broer-Kaup (WBK) equation [5][6][7], reads:…”

Stripe solitons and lump solutions for a generalized Kadomtsev–Petviashvili equation with variable coefficients in fluid mechanics

“…The KP equation can be applied to describe water waves of long wavelength with weakly non-linear restoring forces and frequency dispersion [1]. Particularly, the constant-coefficient KP equations have been studied in many works, such as multi-soliton solutions [2], conservation laws [3], Bilinear forms [4] and lump solutions [5][6][7][8]. However, the variable-coefficient KP equations can furnish more realistic models than the constant-coefficient KP equations [9][10][11][12].…”