conservation laws and invariant solutions of time-dependent calogero-bogoyavlenskii-schiff equation

This paper uses the classical lie method to determine symmetry reductions and exact solutions of the time-dependent calogero-bogoyavlenskii-schiff equation (vcbs). this classical method generates some exact arbitrary solutions and exhibits various qualitative behaviors. here, we derived the infinitesimal symmetries and six basic combinations of vector fields in the linear forms that can be utilized to transform the given equation into the pdes with their variables. further, we obtain comprehensive invariant solutions of the vcbs equation. next, we apply a direct method to explore conservation laws. finally, we determine the conservation laws of the vcbs equation via the bluman-anco homotopy formula.