A Family of Novel Exact Solutions to 2+1-Dimensional KdV Equation

Abstract

We introduce two subequations with different independent variables for constructing exact solutions to nonlinear partial differential equations. In order to illustrate the efficiency and usefulness, we apply this method to $\left(2+1\right)$-dimensional KdV equation, which was first derived by Boiti et al. (1986) using the idea of the weak Lax pair. As a result, we obtained many new exact solutions.