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