Analysis of the Generalized KdV Equation with Variable Coefficients Painleve

Using symbolic computation of the coefficient functions, the generalized KdV equation with variable coefficient functions X and T are Painleve analyzed. Put the solution for the generalized Laurent equation expansion u(x,t)= into equation, coefficient of each power arrangement and it is zero. Get the value of P and UJ on the recurrence relation and the resonance point; by the compatibility conditions of constant we can get the knowledge of original equations with Painleve properties. At the same time using Painleve truncation method the author gives the variable coefficient KdV equation of a Backlund transformation. Since the Backlund transformation is in contact with the solution of a partial differential equation by equation transformation, a solution can be found from another solution of equation, As an example, according to the obtained Backlund transformation given two equations, we can get the exact solution.