Perturbation of the two-soliton solution to the KdV equation

The Cauchy problem for the perturbed Korteveg-de Vries equation with the two-soliton initial data is considered. Differential equations for the slow deformation of the parameters—amplitudes and phase shifts—are derived. It is shown that the phase shift of the slow soliton depends on the deformation of the fast solition. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 1, pp. 92–102.