The generalized Kawahara equation ut= a (t) uxxxxx+ b (t) uxxx+ c (t) f (u) ux appears in
many physical applications. A complete classification of low-order conservation laws and
point symmetries is obtained for this equation, which includes as a special case the usual
Kawahara equation ut= αuux+ βu2ux+ γuxxx+ μuxxxxx. A general connection between
conservation laws and symmetries for the generalized Kawahara equation is derived
through the Hamiltonian structure of this equation and its relationship to Noether's theorem …