<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. The periodic solutions are found using this method which contains both solitary wave and shock wave solutions. In this paper, the new results are computed using the closed-form solution including solitary or shock wave solutions which are obtained using Jacobi elliptic function method. The corresponding solitary or shock wave solutions are compared with the actual results. The results are visualised and the periodic behaviour of the solution is described in detail. The shock waves are found to break with time, whereas, solitary waves are found to be improved continuously with time.</p>
</abstract>

This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. The periodic solutions are found using this method which contains both solitary wave and shock wave solutions. In this paper, the new results are computed using the closed-form solution including solitary or shock wave solutions which are obtained using Jacobi elliptic function method. The corresponding solitary or shock wave solutions are compared with the actual results. The results are visualised and the periodic behaviour of the solution is described in detail. The shock waves are found to break with time, whereas, solitary waves are found to be improved continuously with time.

Travelling Wave Solutions of the Non-Linear Wave Equations

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Travelling Wave Solutions of the Non-Linear Wave Equations"}

This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method. This method is...

Travelling Wave Solutions of the Non-Linear Wave Equations

Published Online: Apr 25, 2023

Page range: 239 - 245

Received: Sep 25, 2022

Accepted: Dec 06, 2022

DOI: https://doi.org/10.2478/ama-2023-0027

Keywords
nonlinear evolution problems, coupled equations, Jacobi elliptic function, periodic solutions

© 2023 Jamil A. Haider et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Travelling Wave Solutions of the Non-Linear Wave Equations

Published Online: Apr 25, 2023

Page range: 239 - 245

Received: Sep 25, 2022

Accepted: Dec 06, 2022

DOI: https://doi.org/10.2478/ama-2023-0027

Keywordsnonlinear evolution problems, coupled equations, Jacobi elliptic function, periodic solutions

© 2023 Jamil A. Haider et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nonlinear evolution problems, coupled equations, Jacobi elliptic function, periodic solutions