Symmetry solutions of the fifth-order non-linear equation with temporal and spatial dispersion terms

The fifth-order non-linear partial differential equations (NPDEs) with temporal and spatial dispersion have been seen in the literature to model optical communication, fluid mechanics, condensed matter, electromagnetic phenomena, and the propagation of pulses in optical fibers. The considered model is not an easily solvable equation because of temporal and spatial dispersion. Our main aim is to obtain the explicit form of exact solutions via a combination of Lie group transformation and ansatz-based methods. Finally, the obtained results, which are novel solutions in explicit form, have been presented to illustrate the physical nature by means of three-dimensional plots, with a discussion of the results.

کلیدواژه ها:

fifth-order non-linear equation ، Exact solutions ، Lie group transformation ، ansatz-based methods ، solitons