Perturbation of the two-soliton solution of the KdV equation

The Cauchy problem for the perturbed Korteveg–de Vries equation with the two-solitons initial data is considered. Differential equations for the slow deformation of the parameters, namely amplitudes and phase shifts, are derived. It is shown that the phase shift of the slow soliton depends on the deformation of the fast soliton. For some perturbations the slow deformations of the parameters are obtained in the explicit form.