Perturbation of a two-soliton solution of the Korteweg–de Vries equation in the case of close amplitudes

We investigate the interaction process for two solitons with close amplitudes under a small perturbation. The leading term of the formal asymptotic solution is found as the sum of two solitons with slowly varying parameters. The equations of slow variations are derived for the soliton phase shifts. The effects related to the interaction between the perturbed solitons can compensate the velocity difference in some conditions, which can result in the formation of the so-called quasi-stationary soliton pair.