On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions

Baoyong Guo; Yong Fang; Huanhe Dong

doi:10.1016/j.heliyon.2023.e15929

On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions

Heliyon. 2023 May 8;9(5):e15929. doi: 10.1016/j.heliyon.2023.e15929. eCollection 2023 May.

Authors

Baoyong Guo¹, Yong Fang¹, Huanhe Dong¹

Affiliation

¹ College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China.

Abstract

In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method. In this process, the Hirota bilinear operator played a significant role. Based on the Hirota bilinear forms, the single soliton solutions and the single periodic wave solutions of these two types of equations were obtained respectively. Meanwhile, the figures of the single soliton solutions and the single periodic wave solutions were plotted. Furthermore, the results shed light on that when the amplitude of water wave approaches 0, the single periodic wave solutions tend to the single soliton solutions. The conclusion has been generalized from (2+1)-dimensional equations to (3+1)-dimensional equations.

Keywords: (2+1)-dimensional generalized fifth-order KdV equation; Extended (3+1)-dimensional Jimbo-Miwa equation; Hirota bilinear operator; Periodic wave solutions; Soliton solutions.