Wave solutions to the combined KdV-mKdV equation via two methods with the Riccati equation

Abstract

The exact traveling wave solutions of the combined kdv-mkdv equation, which are the partial differential equations, were examined using the simple equation method with the Ricci equation and the modified extended tanh-function method. The solutions of the combined kdv-mkdv equation are obtained in terms of hyperbolic functions and trigonometric functions. Some solutions are created in the form of kink waves, which are represented by the two-dimensional graph, the three-dimensional graph, and the contour graph.