Painlevéanalysis,infinite dimensional symmetry group and symmetry reductions for the(2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani equation

The(2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani(KdVSKR)equation is studied by the singularity structure analysis.It is proven that it admits the Painlevéproperty.The Lie algebras which depend on three arbitrary functions of time t are obtained by the Lie point symmetry method.It is shown that the KdVSKR equation possesses an infinite-dimensional Kac–Moody–Virasoro symmetry algebra.By selecting first-order polynomials in t,a finite-dimensional subalgebra of physical transformations is studied.The commutation relations of the subalgebra,which have been established by selecting the Laurent polynomials in t,are calculated.This symmetry constitutes a centerless Virasoro algebra which has been widely used in the field of physics.Meanwhile,the similarity reduction solutions of the model are studied by means of the Lie point symmetry theory.