Solution to Nonlinear Wave and Evolution Equations by Direct Algebraic Method

  • C. B. Okechukwu The West African Examinations Council, (WAEC), Bauchi.
  • J. N. Nnadi Department of Mathematics, Abia State University, Uturu, Nigeria.
  • B. O. Osu Department of Mathematics, Abia State University, Uturu, Nigeria.
  • C. P. Ogbogbo Department of Mathematics, University of Ghana Legon.
DOI: https://doi.org/10.6084/m9.figshare.21814335
Keywords: Nonlinear wave equation, Nonlinear evolution equation

Abstract

This work presents a dynamic and systematic step-by-step method for constructing solitary
wave solutions for non-dissipative nonlinear evolution and wave equations from the real exponential
solutions of the underlying linear equations. The work reviewed the direct algebraic method initially proposed by Hereman et. al. (1985) and employed the methodology in solving Benjamin - Bona - Mahony (RLW) equation and Joseph - Egri (TRLW) equation. By the method which involves using a traveling frame of reference to convert the PDE into an ODE and solving the ODE by algebraic processes; we obtained solutions for the Benjamin - Bona - Mahony and the Joseph - Egri equations. This method was found to be efficient in constructing a single solitary wave solution for non-dissipative evolution equations. The results obtained in
this paper are in agreement with those obtained using other methods.

Published
2023-01-20
How to Cite
Okechukwu, C. B., Nnadi, J. N., Osu, B. O., & Ogbogbo, C. P. (2023). Solution to Nonlinear Wave and Evolution Equations by Direct Algebraic Method. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 8(2), 23 - 37. https://doi.org/10.6084/m9.figshare.21814335
Issue
Vol 8 No 2 (2022)
Section
Articles

Copyright (c) 2023 C. B. Okechukwu, J. N. Nnadi, B. O. Osu, C. P. Ogbogbo

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This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.