Extended group analysis and conservation laws of a class of variable coefficient generalized Kawahara equations
We review and extend the results on the group analysis of a class of generalized Kawahara equations with time-dependent coefficients. First, we provide an overview of the existing literature on Lie symmetries and Lie-invariant solutions of such equations. We then present a complete description of their transformation properties, including admissible, equivalence, and Lie symmetry transformations. For practical applications, we further extend these results by presenting a complete Lie symmetry classification without simplifying the coefficients via equivalence transformations. Lie reductions are then systematically performed, and several exact solutions are constructed. Low-order local conservation laws are exhaustively classified: every equation in this class admits conservation of mass and the squared $L^2$ norm, whereas energy-type conservation laws exist only for specific coefficient branches that align with the cases singled out by the symmetry classification. Finally, the classification results are enhanced by a study of contractions, which link cases of Lie symmetry extensions together with the associated reductions and conservation laws.