A new (3 + 1)-dimensional Painlevé-integrable Sakovich equation: multiple soliton solutions

Abstract

Purpose

This paper aims to develop a new (3 + 1)-dimensional Painlevée-integrable extended Sakovich equation. This paper formally derives multiple soliton solutions for this developed model.

Design/methodology/approach

This paper uses the simplified Hirota’s method for deriving multiple soliton solutions.

Findings

This paper finds that the developed (3 + 1)-dimensional Sakovich model exhibits complete integrability in analogy with the standard Sakovich equation.

Research limitations/implications

This paper addresses the integrability features of this model via using the Painlevée analysis. This paper reports multiple soliton solutions for this equation by using the simplified Hirota’s method.

Practical implications

The study reports three non-linear terms added to the standard Sakovich equation.

Social implications

The study presents useful algorithms for constructing new integrable equations and for handling these equations.

Originality/value

The paper reports a new Painlevée-integrable extended Sakovich equation, which belongs to second-order partial differential equations. The constructed model does not contain any dispersion term such as uxxx.

Citation

Wazwaz, A.-M. (2021), "A new (3 + 1)-dimensional Painlevé-integrable Sakovich equation: multiple soliton solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 9, pp. 3030-3035. https://doi.org/10.1108/HFF-11-2020-0687