Eur. Phys. J. Plus (2021) 136: 399
https://doi.org/10.1140/epjp/s13360-021-01372-5

Regular Article

On the role of $K+L+M$-wave mixing effect in the (2+1)-dimensional KP I equation

College of Mathematics Science, Inner Mongolia Normal University, 010022, Hohhot, People’s Republic of China

^b zhaqilao@imnu.edu.cn

Received: 10 November 2020
Accepted: 28 March 2021
Published online: 16 April 2021

Abstract

The effect of $K+L+M$-wave mixing in the (2+1)-dimensional Kadomtsev–Petviashvili I (KP I) equation is investigated. We give a general auxiliary function to obtain the interaction solutions of KP I equation by the Hirota bilinear method and the long wave limit approach. If we choose different values of K, L, M in the general auxiliary function, we will obtain different types interaction solutions, including superposition of Kth-order lump, L-breather and M-soliton solutions. By strengthening the $K+L+M$-wave mixing parameters, the relation of the parameters is given and the interaction solutions are classified via the formula of the general auxiliary function.