On µ-symmetries, µ-reductions, and µ-conservation laws of Gardner equation

In this study, we represent an application of the geometrical characterization of µ-prolongations of vector fields to the nonlinear partial differential Gardner equation with variable coefficients. First, µ-symmetries and the corresponding µ-symmetry classification are investigated and then µ-reduction forms of the equations are obtained. Furthermore, µ-invariant solutions are determined and µ-conservation laws of Gardner equation are studied.