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

Document Type : Research Paper

Authors

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

2 Kalinga Institute of Industrial Technology, Deemed to be University, Bhubaneswar, Odisha 751024, India.

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, electro-magnetic 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 imply the physical nature by means of three-dimensional plots with result discussion.

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Articles in Press, Accepted Manuscript
Available Online from 21 July 2025
  • Receive Date: 04 December 2024
  • Revise Date: 04 July 2025
  • Accept Date: 20 July 2025