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

Izgi, Zehra Pinar; Sahoo, Subhadarshan

doi:10.22034/cmde.2025.64858.2952

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

Document Type : Research Paper

Authors

¹ Tekirdağ Namık Kemal University, Faculty of Arts and Science, Department of Mathematics, 59030 Merkez-Tekirdağ, Turkey.

² Department of Mathematics and Applied Statistics, School of Applied Sciences, Kalinga Institute of Industrial Technology, Deemed to be University, Bhubaneswar-751024, Odisha, India.

10.22034/cmde.2025.64858.2952

Abstract

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.

Keywords

Main Subjects

Approximation methods and numerical treatment of dynamical systems

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