Dynamics of breather, multi-wave, interaction and other wave solutions to the new (3+1)-dimensional integrable fourth-order equation for shallow water waves

• Published in: International journal of numerical methods for heat & fluid flow Vol. 33; no. 11; pp. 3734 - 3747
• Main Author: Wang, Kang-Jia
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 31.10.2023; Emerald Group Publishing Limited
• Subjects: Breathers; Computation; Nonlinear equations; Partial differential equations; Shallow water; Shallow water waves; Traveling waves; Water waves; Multiwave solution; Interaction solution; Breather solution; Ansatz function method; Subequation method
• ISSN: 0961-5539; 0961-5539; 1758-6585
• DOI: 10.1108/HFF-07-2023-0385

Purpose The purpose of this paper is to study the new (3 + 1)-dimensional integrable fourth-order nonlinear equation which is used to model the shallow water waves. Design/methodology/approach By means of the Cole–Hopf transform, the bilinear form of the studied equation is extracted. Then the ansatz function method combined with the symbolic computation is implemented to construct the breather, multiwave and the interaction wave solutions. In addition, the subequation method tis also used to search for the diverse travelling wave solutions. Findings The breather, multiwave and the interaction wave solutions and other wave solutions like the singular periodic wave structure and dark wave structure are obtained. To the author’s knowledge, the solutions obtained are all new and have never been reported before. Originality/value The solutions obtained in this work have never appeared in other literature and can be regarded as an extension of the solutions for the new (3 + 1)-dimensional integrable fourth-order nonlinear equation.