This paper is devoted to obtaining the multi-soliton solutions, high-order breather solutions and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by applying the Hirota bilinear method and the long-wave limit approach. Moreover, the interaction solutions are constructed by choosing appropriate value of parameters, which consist of four waves for lumps, breathers, rouges and solitons. Some dynamical characteristics for the obtained exact solutions are illustrated using figures.
In this paper, new trial functions are constructed via extended “3-3-2-3-1” and “3-3-2-3-2-1” network models based on the bilinear neural networks method. The new lump-type solution, interaction solution, plentiful arbitrary function solutions and periodic lump solutions of the dimensionally reduced [Formula: see text]-generalized Burgers–Kadomtsev–Petviashvili equation are solved. To analyze the dynamic properties of the solutions, appropriate parameters and different activated functions are defined in arbitrary function solutions. Through the three-dimensional and density plots, the dynamical characteristics of the solutions are shown well.
We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N(N +1)−2 in x, y and t by a polynomial of degree 2N(N +1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.
Kadomtsev–Petviashvili equation: One-constraint method and lump pattern
