The general bilinear techniques for studying the propagation of mixed-type periodic and lump-type solutions in a homogenous-dispersive medium

Jian-Guo Liu,Dumitru Baleanu,Li Zhou,Mohamed S Osman,Wen-Hui Zhu

doi:10.1063/5.0019219

Abstract

This paper aims to construct new mixed-type periodic and lump-type solutions via dependent variable transformation and Hirota’s bilinear form (general bilinear techniques). This study considers the (3 + 1)-dimensional generalized B-type Kadomtsev–Petviashvili equation, which describes the weakly dispersive waves in a homogeneous medium in fluid dynamics. The obtained solutions contain abundant physical structures. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D plots.

Highlights

Nonlinear phenomena are investigated in many disciplines of science, such as marine engineering, fluid dynamics, plasma physics, chemistry, applied mathematics, and so on.1–19 With the development of nonlinear dynamics, the research of nonlinear partial differential equations (NPDEs) becomes more and more important
II gives the new mixedtype periodic solutions for the (3 + 1)-dimensional generalized BKP equation based on the dependent variable transformation and Hirota’s bilinear form
As can be seen from the above solution process, the direct test function is very effective for solving the mixed-type periodic solutions of NPDEs

Summary

INTRODUCTION

Scitation.org/journal/adv which describe the interaction between two different types of soliton waves. Multiple-soliton solutions are generated and discussed by Ma.. Tang obtained new analytical solutions that contain different wave structures such as periodic soliton, kinky periodic solitary, and periodic soliton solutions by using the extended homoclinic test approach. By employing the improved (G′/G)-expansion method with the aid of symbolic computations, Chen and Ma 55 obtain new soliton solutions of Eq (1). This paper is organized as follows: Sec. II gives the new mixedtype periodic solutions for the (3 + 1)-dimensional generalized BKP equation based on the dependent variable transformation and Hirota’s bilinear form.

NEW MIXED-TYPE PERIODIC SOLUTIONS

LUMP-TYPE SOLUTIONS

CONCLUSION