Stability and Chaotic Analysis of Nonlinear Fractional Model Using Novel Analytical Technique: Soliton Solutions for Wazwaz Kaur Boussinesq Equation

This study examines the exact solutions of the nonlinear WazwazKaur Boussinesq (NLWKB) equation in (2+ 1)-dimension by using a novel modified (G /G2)-expansion method. This examination uses BetaDerivative, M-Truncated and Conformable derivatives for finding new closed-form soliton solutions. The graphic demonstration covers some of these solutions. These visualized graphs show individual W-type, bright, and dark solitons to emphasize the effect of fractional derivatives on the behavior of waves. Furthermore, the study investigates the bifurcation analysis, chaotic dynamics, multistability, and Poincaré maps to describe the stability transitions of the system. The results illustrate how fractional calculus improves soliton modeling and nonlinear wave propagation, with possible applications in plasma physics, optical fiber communications, ion-acoustic, magneto-sound, and stationary media, and wave dynamics in complex media, and the transmission of tidal and tsunami waves. The proposed method proves to be a powerful method for solving nonlinear fractional models and examining their dynamic behavior