AUTO-BCKLUND TRANSFORMATION AND EXACT TRAVELLING WAVE SOLUTIONS FOR TWO NONLINEAR EVOLUTION EQUATIONS

Explicit exact travelling wave solutions to the KdV equation and the compound KdV-Burgers equation are obtained by combining the truncated Painleve expansion and the different solutions of the Painleve-Bcklund equations.The auto-Bcklund transformations for this two equations are also presented.This method also can be applied to construct the exact travelling wave solutions to other nonlinear evolution equations.