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This study applies the extended Wang’s direct mapping method to the fourth-order (2+1)-dimensional nonlinear Schrödinger equation (NLSE) with Kerr-law nonlinearity and a conformable derivative, relevant to optical fiber technology. The research primarily aims to derive various soliton solutions, including bright, singular, wave, mixed dark-bright, and dark solitons, for this extended equation. By utilizing bifurcation and chaos theories, we explore the dynamics of the associated planar system, examining critical points and how slight changes in parameters can trigger transitions from stable configurations to chaotic behavior. Sensitivity analysis is performed under various initial conditions, revealing that the model exhibits high sensitivity. A detailed analysis of the temporal parameter and conformable derivative is presented through two-dimensional and three-dimensional visualizations. The present soliton solutions are novel and have not been reported in the literature. Another novelty of this work is the application of bifurcation, chaos, and sensitivity analysis to the present nonlinear Schrödinger equation.
Omar et al. (Tue,) studied this question.