Novel solitary wave solutions of the (3+1)–dimensional nonlinear Schrödinger equation with generalized Kudryashov self–phase modulation

This paper investigates the (3+1)-dimensional nonlinear Schrö dinger equation, incorporating cross-spatial dispersion and a generalized form of Kudryashov's self-phase modulation. Using the generalized Jacobi elliptic method, we systematically derive novel soliton solutions expressed in terms of Jacobi elliptic and Weierstrass elliptic functions, providing deeper insights into wave dynamics in nonlinear optical media. The obtained solutions exhibit diverse structural transformations governed by the parameter (n) known as full nonlinearity, encompassing optical bullet solutions, optical domain wall solutions, singular solitons, and periodic solutions. Furthermore, we discuss the potential experimental realization of these solitonic structures in ultrafast fiber lasers and nonlinear optical systems, drawing connections to recent experimental findings. To facilitate a comprehensive understanding of their physical properties, we present detailed three-dimensional (3D), two-dimensional (2D), and contour visualizations, highlighting the interplay among dispersion, nonlinearity, and self-modulation effects. These results offer new perspectives on soliton interactions and have significant implications for optical communication, signal processing, and nonlinear wave phenomena.