Group Classification of Variable Coefficient $K(m,n)$ Equations

Abstract

Lie symmetries of $K(m,n)$ equations with time-dependent coefficients are classified. Group classification is presented up to widest possible equivalence groups, the usual equivalence group of the whole class for the general case and the conditional equivalence groups for special values of the exponents $m$ and $n$. Examples on reduction of $K(m,n)$ equations (with initial and boundary conditions to nonlinear ordinary differential equations (with initial conditions) are presented.