Analytical Wave Structures of the (3+1)-Dimensional Perturbed NLSE Incorporating Cubic-Quintic Nonlinearity and Spatio-Temporal Dispersion

This study consists of the soliton dynamics governed by the (3 + 1)-dimensional perturbed nonlinear Schrödinger equation incorporating cubic-quintic nonlinearity and spatio-temporal dispersion. This generalized form of the nonlinear Schrödinger equation is particularly relevant for describing the propagation of ultrashort optical pulses in nonlinear media, wherein conventional dispersion mechanisms are negligible, and higher-order and nonlinear phenomena predominate. To derive optical solitons, the addendum of Kudryashov's method is employed. By imposing appropriate constraints on the system parameters, the necessary conditions for the emergence of distinct optical soliton structures are established. The obtained results offer substantial theoretical insights into the intricate dynamics of pulse propagation in advanced photonic environments, with potential applications in the development and refinement of nonlinear optical waveguides and fiber-optic communication systems.