Bifurcation analysis and dynamical behavior of novel optical soliton solution of chiral (2 + 1) dimensional nonlinear...

This study explores in detail the bifurcation and optical solitons of the third-order nonlinear chiral (2 + 1)-dimensional nonlinear Schrödinger equation (M-fCNLSE) with the M-fractional derivative in nonlinear media. We also discuss the properties of fractional derivatives in this context. Initially, bifurcation theory is utilized to analyze critical points and phase portraits, identifying transitions that give rise to new dynamical behaviors, such as stability shifts or the onset of chaotic motion. The first figure depicts the dynamics of soliton solutions undergoing a saddle-node bifurcation. There are two techniques, namely the polynomial expansion (PE) and the unified solver (US) techniques, that are applied to explore wave propagation in telecommunication systems, nonlinear optics, plasma physics, and quantum mechanics. These methods enable the creation of new optical soliton solutions using hyperbolic, rational, and trigonometric functions. Numerical results, presented in 2D and 3D diagrams, demonstrate the behavior of the solutions. The polynomial expansion technique generates diverse periodic optical soliton solutions, including double-periodic and lump wave solitons. The unified solver technique produces periodic breather waves, double-periodic waves, and other complex wave structures. Additionally, two-dimensional graphs display the effects of the truncated M-fractional parameters for [Formula: see text]. Overall, this investigation and the proposed techniques provide valuable tools for generating precise optical soliton solutions, which have significant applications in optical communications, nonlinear optics, and engineering.