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In this paper, the nonlinear Rosenau-Hyman equation with time dependentvariable coefficients is considered for investigating its invariant properties,exact solutions and conservation laws. Using Lie classical method, we derivesymmetries admitted by considered equation. Symmetry reductions are performedfor each components of optimal set. Also nonclassical approach is employed onconsidered equation to find some additional supplementary symmetries andcorresponding symmetry reductions are performed. Later three kinds of exactsolutions of considered equation are presented graphically for differentparameters. In addition, local conservation laws are constructed for consideredequation by multiplier approach.

On exact solutions, conservation laws and invariant analysis of the generalized Rosenau-Hyman equation