Painleve analysis and similarity solutions to the (2+1)-dimensional nonlinear evolution equation

The singularity analysis and symmetry reductions of the new (2+1)-dimensionaJ nonlinear evolution equation, u(ty) + uu(xy) - u(x)u(y) - gammau(xxy) = 0, arising in a one-dimensional model for the three-dimensional vorticity equation are investigated in this paper. The singularity analysis of the equation is performed by using the WTC method such that it is shown that the equation fails to pass Painleve test. And then the CK direct method is extended to reduce this equation. As a consequence, eleven families of (1+1)-dimensional symmetry reductions of the equation are obtained which are useful to further seek the exact solutions of the equation.