To read this content please select one of the options below:

New (3+1)-dimensional integrable fourth-order nonlinear equation: lumps and multiple soliton solutions

Abdul-Majid Wazwaz (Department of Mathematics, Saint Xavier University, Chicago, Illinois, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 9 August 2021

Issue publication date: 19 April 2022

213

Abstract

Purpose

This paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t. The new equation models both right- and left-going waves in a like manner to the Boussinesq equation.

Design/methodology/approach

This formally uses the simplified Hirota’s method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space.

Findings

This paper confirms the complete integrability of the newly developed (3 + 1)-dimensional model in the Painevé sense.

Research limitations/implications

This paper addresses the integrability features of this model via using the Painlevé analysis.

Practical implications

This paper presents a variety of lump solutions via using a variety of numerical values of the included parameters.

Social implications

This work formally furnishes useful algorithms for extending integrable equations and for the determination of lump solutions.

Originality/value

To the best of the author’s knowledge, this paper introduces an original work with newly developed integrable equation and shows useful findings of solitons and lump solutions.

Keywords

Acknowledgements

Compliance with ethical standards.

Conflict of interest: The author declares that he has no conflict of interest.

Citation

Wazwaz, A.-M. (2022), "New (3+1)-dimensional integrable fourth-order nonlinear equation: lumps and multiple soliton solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 5, pp. 1664-1673. https://doi.org/10.1108/HFF-05-2021-0318

Publisher

:

Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

Related articles