Quantum-mechanical properties of long-lived optical pulses in the fourth-order KdV-type hierarchy nonlinear model

Abstract

This study aims to investigate the (3+1)-dimensional fourth-order KdV-type hierarchy nonlinear equation. For this aim, we use Hirota's simple method to handle one, two, three, and four soliton solutions. Furthermore, using the ansatz method in the form of the tanh(p) function, the symbolic computational method is used to construct kink solitary wave solutions, multi-wave solutions, X -type solitons, and Y -type solitons, as well as shock wave solutions. Furthermore, the physical structure and propagation characteristics of the obtained solutions are simulated.