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.
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.
The developed extended Sakovich models exhibit complete integrability in analogy with the original Sakovich equation.
This paper is to address these two main motivations: the study of the integrability features and solitons solutions for the developed methods.
This paper introduces two Painlevé-integrable extended Sakovich equations which give real and complex soliton solutions.
This paper presents useful algorithms for constructing new integrable equations and for handling these equations.
This paper gives two Painlevé-integrable extended equations which belong to second-order PDEs. The two developed models do not contain the dispersion term uxxx. This paper presents an original work with newly developed integrable equations and shows useful findings.
