In this article, we present the general form of conservation laws for the nonlinear Rosenau–Hyman compacton $K(m, n)$ equations using multiplier’s approach. General formulas for some new conservation laws are established for the $K(m, n)$ equations. We describe three different cases where Lie symmetries are associated with these generalised conservation laws. The double reduction theory is utilised to construct some new reductions and exact solutions for different values of $m$ and $n$.
