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

Yusuf Pandir; Ali Ekin

doi:10.61383/ejam.20231130

Authors

Yusuf Pandir Email Department of Mathematics, Faculty of Arts and Sciences, Yozgat Bozok University, 66100 Yozgat/Turkey Corresponding Author
Ali Ekin Email 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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