On the Soliton Structures of the (2+1)-Dimensional Long Wave-Short Wave Resonance Interaction Equation with Two Analytical Techniques and its Bifurcation Analysis

Abstract

The (2+1)-dimensional long-wave-short-wave resonance interaction (LWSWRI) equation has extensive applications in various fields of science and engineering. The (2+1)-dimensional LWSWRI equation and two analytical techniques have been considered in this manuscript. These schemes, via the advanced auxiliary equation, improve F-expansion techniques applied to the considered model and obtain soliton solutions with a lot of parameters. These derived soliton solutions manifest as trigonometric, hyperbolic, rational, and exponential function solutions, highlighting their utility as mathematical tools. The study offers visual representations, including both three-dimensional (3D) and two-dimensional (2D) combined charts, to illustrate selected solutions and demonstrate the influence of parameters. Furthermore, the bifurcation analysis (BA) of the model is studied through the planar dynamical systems. The stability of the equilibrium points (EPs) and a graphical representation of the phase chart of the system are investigated. The Hamiltonian function is also derived in this manuscript. These methodologies function as dependable, straightforward, and powerful instruments for examining diverse nonlinear evolution equations encountered in physics, applied mathematics, engineering, and other disciplines. GANITJ. Bangladesh Math. Soc. 44.1 (2024) 59-76