Two new Painlevé-integrable extended Sakovich equations with (2 + 1) and (3 + 1) dimensions

Abstract

Purpose

The purpose of this paper is to introduce two new Painlevé-integrable extended Sakovich equations with (2 + 1) and (3 + 1) dimensions. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models.

Design/methodology/approach

The newly developed Sakovich equations have been handled by using the Hirota’s direct method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions.

Findings

The developed extended Sakovich models exhibit complete integrability in analogy with the original Sakovich equation.

Research limitations/implications

This paper is to address these two main motivations: the study of the integrability features and solitons solutions for the developed methods.

Practical implications

This paper introduces two Painlevé-integrable extended Sakovich equations which give real and complex soliton solutions.

Social implications

This paper presents useful algorithms for constructing new integrable equations and for handling these equations.

Originality/value

This paper gives two Painlevé-integrable extended equations which belong to second-order PDEs. The two developed models do not contain the dispersion term u_xxx. This paper presents an original work with newly developed integrable equations and shows useful findings.

Citation

Wazwaz, A.-M. (2020), "Two new Painlevé-integrable extended Sakovich equations with (2 + 1) and (3 + 1) dimensions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 3, pp. 1379-1387. https://doi.org/10.1108/HFF-08-2019-0652