A NEW TRIAL FUNCTION TECHNIQUE AND ITS APPLICATIONS TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
Keywords:
dual trial function technique, KdV-Burgers equation, KdV-Burgers-Kuramoto equation, Kuramoto-Sivashinsky equation, travelling wave solution, single wave solutionDOI:
https://doi.org/10.17654/0972096025008Abstract
In this article, by bringing in a nonlinear transformation containing two trial functions, we put forward a new trial function technique named as a dual trial function technique to search for the explicit and accurate travelling wave solutions of NPDEs. In order to illustrate the feasibility of this technique, we apply it to solve the KdV-Burgers equation, KdV-Burgers-Kuramoto equation and Kuramoto-Sivashinsky equation. As a result, a lot of more general explicit and accurate travelling wave solutions of these three equations, including the single wave solutions and the singular travelling wave solutions, etc, are successfully constructed in a systematic and simple way. The obtained solutions are the same as those given in the existing references. In addition, compared with the proposed approaches in the existing references, the technique described herein appears to be less calculative. Our technique may provide a novel way of thinking for solving NPDEs. Furthermore, it is worth noting that our dual trial function technique is different from the existing trial function method containing one trial function. Compared with the existing trial function method, our technique is of certain advantages that this technique is more flexible and convenient for solving NPDEs and that it can be applied to search for the explicit and accurate travelling wave solutions of more NPDEs. It is our firm conviction that the procedure used herein can be utilized to search for the explicit and accurate travelling wave solutions of other NPDEs as well. We try to generalize this technique to search for the explicit and accurate travelling wave solutions of other NPDEs.
Received: April 7, 2025
Revised: May 15, 2025
Accepted: July 1, 2025
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