Analytical and algebraic insights to the generalized Rosenau equation: Lie symmetries and exact solutions

In this article we attempted to perform a group-theoretical analysis of a Rosenau equation with a general nonlinearity. We determined certain classes of equations with associated Lie group of transformations and corresponding Lie algebras. For these specific classes, we performed reductions to ordinary differential equations through the optimal system of one-dimensional subalgebras. Further, considering cubic, quintic and cubic–quintic nonlinearities we found some exact solutions of hyperbolic and elliptic type. We also derived Rosenau equations with power-law and exponential type nonlinearities via physical considerations, which well matched with the families of equations suggested by the Lie symmetry classification.