A DIRECT APPROACH TO THE SOLITON PERTURBATION FOR KdV-MKdV EQUATION

Abstract The authors develop a direct approach to the soliton perturbation based on the separation of variables. With the aid of approach, the first-order effects of perturbation on a KdV-MKdV soliton are derived, both the slow time-dependence of the soliton parameters and the first-order correction are obtained.