Conservation laws and exact solutions of a family of compacton-supporting equations

In this article, we study a generalized equation that represents a family of compacton-supporting equations. We present the general form of conservation laws for the family of compacton equations by employing the multiplier approach. The generalized conservation laws presented in this study are important in determining the solution process of any third-order nonlinear dispersive partial differential equation that belongs to the category of the generalized compacton family equation. The double reduction theory is employed to construct reductions and new exact solutions of various sub-cases of the compacton family equation.