On the role of -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
Accepted: 28 March 2021
Published online: 16 April 2021
The effect of -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 -wave mixing parameters, the relation of the parameters is given and the interaction solutions are classified via the formula of the general auxiliary function.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021