Group analysis of a class of generalized Kawahara equations

Abstract:
We study generalized Kawahara equations $$ u_t+\alpha(t)f(u)u_x+\beta(t)u_{xxx}+\sigma(t)u_{xxxxx}=0, $$ from the Lie symmetry point of view. Here $n$ is an arbitrary nonzero integer, $f$, $\alpha$, $\beta$ and $\sigma$ are smooth nonvanishing functions of their variables. The equivalence groupoid of the class is constructed and then the exhaustive group classification is presented.