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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Pandır et al. (2023) studied this question.
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