On the Characteristic Problem of the Revised KdV Equation

Abstract:

      [5] studied the solution of isolated wave of the revised KdV equation u_t + auu_x + au²u_x +μu_x³= 0. For the characteristic problem of revised KdV equation. This paper designs a structure and gets an integral differential equation, which is equivalent to the revised KdV equation by means of Green formula and the conditions of definite solution.Using the principle of the fixed point and the sequence of the integral differential equation, we get the iteration solution of uniform converge of the characteristic problem of the revised Kdv equation on Ω.