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

Abstract

The primary goal of this article is to extend previous results and obtain a more comprehensive variety of analytical wave solutions to the (2 + 1)-dimensional Sakovich equation, a nonlinear evolution equation that plays a remarkable role in condensed physics, fiber optics, and fluid dynamics. By employing two relatively new techniques, Lie symmetry analysis, and the extended Jacobian elliptic function expansion method, some standard form of new and unique closed-form solutions are established in terms of trigonometric, hyperbolic, and Jacobi elliptic functions. An optimal system of the one-dimensional subalgebras is also constructed using Lie vectors. These generated solutions contain several ascendant parameters that play a crucial role in describing the inner mechanism of a given physical model. Therefore, the obtained wave solutions are demonstrated graphically by three- and two-dimensional graphics using Mathematica. In addition, a couple of varieties of solutions, including multi soliton, periodic soliton, Bell-shaped, and parabolic profile, are depicted for the suitable values of the included parameters. Finally, it must be noted that the variation in obtained wave profiles by the change in subsidiary involved parameters reveals the parameter effects on the wave. The derived solutions are more generalized than previous established results (Özkan and Yaşar in Alex Eng J 59:(6):5285–5293, 2020), showing the novelty and significance of our solutions. Also, the solutions obtained in the form of Jacobi elliptic functions have never been reported in the literature. This study ensures that the forgoing techniques are practical and may be used to seek the solitary solitons to a diversity of nonlinear evolution equations.