Symmetry and Painlevé analysis for the extended Sakovich equation

Abstract

Purpose The purpose of this paper is to concern with introducing symmetry analysis to the extended Sakovich equation. Design/methodology/approach The newly developed Sakovich equation has been handled by using the Lie symmetries via using the Lie group method. Findings The developed extended Sakovich model exhibit symmetries and invariant solutions. Research limitations/implications The present study is to address the two main motivations: the study of symmetry analysis and the study of soliton solutions of the extended Sakovich equation. Practical implications The work introduces symmetry analysis to the Painlevé-integrable extended Sakovich equation. Social implications The work presents useful symmetry algorithms for handling new integrable equations. Originality/value The paper presents an original work with symmetry analysis and shows useful findings.

Diverse analytical wave solutions and dynamical behaviors of the new (2 + 1)-dimensional Sakovich equation emerging in fluid dynamics

“…The four equations, Sakovich equation (1) , and the three developed equations ( 5), ( 6) and (7), were proved to be Painlevé integrable where multiple soliton solutions were derived by examining resonance points and compatibility conditions. The popularity of Sakovich equations has resulted in the development of new (2 + 1)-dimensional extension [21] that is…”

“…Wang et.al. [21] proposed the Lie symmetry approach to obtain invariant solutions of the equation ( 8). Özkan et.al.…”

A new Painlevé integrable Broer-Kaup system: symmetry analysis, analytic solutions and conservation laws

“…In Section 3, Lie classical method (for detailed study, one can refer Bluman George and Cole Julian, 2012; Olver, 2000;Bluman George and Kumei, 2013;Kumari et al, 2020;Osman et al, 2020;Wang and Wazwaz, 2020;Kumar and Manju, 2020) is used to find point symmetries of the proposed system (1). It follows the similarity reductions which subsequently yields group invariant solutions.…”

Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation

“…e Lie symmetry method presented by Lie [9] is one of the well-known methods for obtaining exact solutions of nonlinear PDEs. Up to now, the Lie symmetry method has been applied to a number of mathematical and physical models, see [10][11][12][13][14] and references therein. is method is effective to get similarity solutions and solitary wave solutions of NPDEs.…”