THE SERIES SOLUTION FOR KORTEWEG-DEVRIES-BURGERS EQUATION

The search of the propagating wave solution of KdV-Burgers equation can be reduced to the solution of the following boundary value problem d2u/dz2 - A(m)du/dz + u2 - u = 0, u(-infinity) = 1, u(+ infinity) = 0. Its series solution is given in the present paper. We first find three different series solutions which all satisfy the equation in three intervals, and then construct a global solution using the connection conditions (keeping the continuity of function and its first order derivative). The exact solution and the series solution are in good agreement at any decimal place. The corresponding series solution is obtainable for any value of the parameter A(m). Especially, for the first time. the series solutions with oscillating shock profiles are obtained for the case of A(m)<2.