Lie symmetry analysis, exact solutions, conservation laws of variable-coefficients Calogero-Bogoyavlenskii-Schiff equation

In this paper, a (2 + 1)-dimensional variable-coefficients Calogero-Bogoyavlenskii-Schilf (vcCBS) equation is studied. The infinitesimal generators and symmetry groups are obtained by using the Lie symmetry analysis on vcCBS. The optimal system of one-dimensional subalgebras of vcCBS is computed for determining the group-invariant solutions. On this basis, the vcCBS is reduced to two-dimensional partial differential equations (PDEs) by similarity reductions. Furthermore, the reduced PDEs are solved to obtain the two-soliton interaction solution, the soliton-kink interaction solution and some other exact solutions by the (G'/G)-expansion method. Moreover, it is shown that vcCBS is nonlinearly self-adjoint and then its conservation laws are calculated.