Week interaction of the perturbed Korteveg–de Vries solutions

The Cauchy problem for the perturbed Korteveg–de Vries equation with the $N$-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 solitons depends on the deformation of the fast solitons. This result is interpreted as weak interaction of the solitons with the soliton tails.