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

Abstract

Under investigation, this paper constructs an improved and comprehensive class 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 applying relatively, two renewed techniques named Lie symmetry analysis and extended Jacobian elliptic function expansion method, some standard class of new and wide-spectrum closed-form solutions are established in terms of trigonometric, hyperbolic, and Jacobi elliptic functions. These ascertained 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 parameters reveals the parameter effects on the wave. 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 (NLEEs).

Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

“…Solitons also matter significantly as they are pivotal for the advancement of computer systems' computing power, while they present a wide variety of applications. Such applications cover image processing, data analysis, neurology, and fluids, among other fields [1][2][3]. As a result, experts have actively explored the evolution of soliton solutions for nonlinear partial differential equations (NLPDEs).…”

Novel Soliton Solutions for the (3 + 1)-Dimensional Sakovich Equation Using Different Analytical Methods

“…Finding the precise solutions of the pertinent NLEEs is crucial for improving our comprehension of nonlinear phenomena and their application to practical problems. A lot of various strategies for obtaining exact solutions to NLEEs have been introduced such as Hirota's method [1][2][3], Bäcklund transformation method [4], He-Laplace variational iteration method [5], modifed homotopy perturbation method [6], Lie symmetry analysis [7,8], the extended tanh method [9], and numerous other techniques [10][11][12]. A very important model with wide applications in diferent felds is the (2 + 1)-dimensional second-order Sakovich equation, which can be used to interpret the dynamics of the water waves in an elongate, limited, hollow duct.…”

“…Many researchers present investigated this equation using various techniques such as kumar et al employ Lie symmetry analysis and extended Jacobian elliptic function expansion method [11], Saglam Ozkan and Yasar employed the logarithmic transformation with the ansatz function technique [15], the new modifed extended direct algebraic (NMEDA) technique is used by Younis et al [16], and Shailendra Singh et al solved the equation with variable coefcients [17] employing the Painlevé analysis and auto-Bäcklund transformation methods.…”