Eur. Phys. J. Plus (2018) 133: 116
https://doi.org/10.1140/epjp/i2018-11945-8

Regular Article

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

¹ School of Mathematics and Statistics, Beijing Institute of Technology, 100081, Beijing, China
² School of Mathematical and Statistics, Hebei University of Economics and Business, 050061, Shijiazhuang, China
³ Department of Mathematics, Yuxi Normal University, 653100, Yuxi, China

^* e-mail: wei12345yi@126.com

Received: 17 December 2017
Accepted: 19 February 2018
Published online: 20 March 2018

Abstract

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.