Generalized conditional symmetry and solutions to nonlinear diffusion equations with variable coefficients

Using generalized conditional symmetry method to research a kind of nonlinear diffusion equations with variable coefficients.When the diffusion term is taken in the form D(u)=um(m≠-1,0,1),this equation is discussed,some exact solutions to the equation are obtained.The exact solutions are the solutions of the functional separation of variables in the form,they can be seen as a special form of generalized functional separation of variables solutions.These exact solutions have a rich theoretical and practical significance,and deepen and develop the scope of solutions of such equation.