New solitary wave solutions of the Korteweg-de Vries (KdV) equation by new version of the trial equation method

Authors

  • Yusuf Pandir Department of Mathematics, Faculty of Arts and Sciences, Yozgat Bozok University, 66100 Yozgat/Turkey
  • Ali Ekin The Graduate School of Natural and Applied Sciences, Yozgat Bozok University, 66100 Yozgat, Turkey

DOI:

https://doi.org/10.61383/ejam.20231130

Keywords:

New version of the trial equation method, nonlinear partial differential equations, Korteweg-de Vries (KdV) equation, solitary wave soliton solutions

Abstract

New solitary wave solutions for the Korteweg-de Vries (KdV) equation by a new version of the trial equation method are attained. Proper transformation reduces the Korteweg-de Vries (KdV) equation to a quadratic ordinary differential equation that is fully integrated using the new version trial equation approach. The family of solitary wave solutions of the reduced equation ensures a combined expression for the Korteweg-de Vries (KdV) equation, which contains exact solutions derived in recent years using different integration methods. The analytic solution of the reduced equation permits to find exact solutions for the Korteweg-de Vries (KdV) equation, providing a variety of new solitary wave solutions that have not been reported before.

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Published

2023 May 09

How to Cite

[1]
Y. Pandir and A. Ekin, “New solitary wave solutions of the Korteweg-de Vries (KdV) equation by new version of the trial equation method”, Electron. J. Appl. Math., vol. 1, no. 1, pp. 101–113, May 2023.

Issue

Section

Research Article
Received 2023 Mar 15
Accepted 2023 May 04
Published 2023 May 09

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