Lie group analysis and novel solutions for the generalized variable-coefficients Sawada-Kotera equation

¹ College of Business Administration in Majmaah, Majmaah University - Majmaah 11952, Kingdom of Saudi Arabia
² Department of Mathematics, Faculty of Education, Ain Shams University - Cairo, Egypt
³ Department of Physics, College of Science at Al-Zulfi, Majmaah University - Al-Zulfi 11952, Kingdom of Saudi Arabia
⁴ Geomagnetic and Geoelectric Department, National Research Institute of Astronomy and Geophysics (NRIAG) 11421 Helwan, Cairo, Egypt

^(a) E-mail: r.abdelhaim@mu.edu.sa (corresponding author)

Received: 12 January 2023
Accepted: 18 January 2023

Abstract

In this paper, the generalized fifth-order variable-coefficients Sawada-Kotera equation arising in coastal seas, fjords, lakes, and the atmospheric boundary layer is studied by using the symmetry method. As a result, four-vector fields are obtained and a commutative Lie group of transformations. Then, by using suitable combinations of the Lie vector fields three distinct similarity reductions in the form of nonlinear ordinary differential equations are yielded. By solving the reduced equations using the known techniques and the Jacobi expansion method many novel periodic and solitary wave solutions are considered. From a physical point of view, the dynamic behavior of two distinct wave structures, periodic and kink soliton, was investigated for different choices of the variable coefficients and it was clear that the wave propagation shape is affected by the change of the variable function.