Chaotic analysis, hopf bifurcation and collision of optical periodic solitons in (2+1)-dimensional degenerated Biswas–Milovic equation with Kerr law of nonlinearity

The main aim of this research study is to examine optical soliton phenomena in a (2+1)-dimensional Schrödinger class nonlinear model that degenerates from Biswas-Milovic equation (BME) using Riccati modified extended simple equation method (RMESEM). This model has particular relevance in the fiber optics domain. The proposed anstaz RMESEM uses a complex structured wave transformation to produce nonlinear ordinary differential equation (NODE) and constraint conditions for Kerr law nonlinearity form of the model. The resulting NODE is assumed to have a closed form solution that converts it into a system of nonlinear algebraic equations via substitution in order to determine fresh variety of optical soliton solutions. The final visualizations of the obtained optical soliton solutions in the form of 3D, contour, and 2D forms demonstrate that the model develops Hopf bifurcation, rogue and internal envelope solitons as a result of the elastic and inelastic collision of optical periodic solitons while the norms of the obtained optical soliton reveal dark and bright kink structures. Using phase portraits and time-series maps, we also study bifurcating and chaotic behavior, observing its presence in the perturbed dynamical system and obtaining favorable results indicating Hopf bifurcation and periodicity. We use a generalized trigonometric function to perturb the planner system for the first time in order carry out chaotic analysis. Furthermore, our results are analyzed and linked to the soliton dynamics in BME, demonstrating the effectiveness of the suggested method as an effective method of identifying novel soliton phenomena within such nonlinear settings.