Investigating innovative optical solitons for a (3+1)- dimensional nonlinear Schrödinger’s equation under the influences of 4th-order dispersive and parabolic law of nonlinearities

This study tackles a nonlinear Schrödinger’s equation in three dimensions, using three dispersive components of fourth order, often resulting in pure-quartic solitons. Pure-quartic bullets are known to deviate from conventional solitons due to their balance of fourth-order dispersion and nonlinearity. As bright and dark optically modulated bullets, we derive many solutions. Experiments on bullet transmission using optical nanofibers can benefit from the solutions found. Our creative solutions are produced by implementing the well-known scheme which is the improved modified extended tanh-function scheme. We find novel kinds of solutions (dark, bright, singular solitons, exponential, singular periodic, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic functions) that make their originality for the problem at hand evident by using the previously described approach. Contour plots and 2D and 3D visualizations in Wolfram Mathematica software are used to show how the well-furnished results propagate for various values of the necessary free parameters. The results demonstrate the computational processes’ precise, well-informed, and efficient nature. Through their integration with representational computations, they may be applied to increasingly complex phenomena. This work constitutes a major advancement in our comprehension of the intricate and erratic behavior of this mathematical model.