N-soliton, M-breather and hybrid solutions of a time-dependent Kadomtsev-Petviashvili equation

In this paper, the Hirota bilinear method for the standard Kadomtsev-Petviashvili (KP) equation is extended to a recently proposed time-dependent KP equation. Firstly, general N-soliton solutions of this equation are derived by introducing a new property of the bilinear operator. Secondly, imposing parameter constraints in the N-soliton solutions, M-breather solutions and hybrid ones composed of solitons and breathers are constructed, respectively. Thirdly, by choosing proper time-dependent coefficients, some figures are given to shed light on the dynamic properties of the obtained solutions. These results show that the time-dependent coefficients can bring many different dynamic behaviors, which theoretically indicates that the time-dependent KP equation might be physically important to describe certain phenomena in the nature.(c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.