Generation of soliton pairs in nonlinear media with weak dissipation

Weak interaction processes are studied for two KdV solitons at low viscosity. A model is suggested for describing the interaction in terms of slowly varying parameters of the exact two-soliton solution to the KdV equation under perturbation. It is shown that both the inverse scattering problem method and the Witham method lead to the same system of reduced equations. The resulting solutions are in good agreement with numerical calculation data. The main effect is the formation of a bound quasistationary soliton pair and its subsequent dissipation. It turns out that although both the process of soliton merger and the process of dissipation are due to low viscosity, the former is substantially faster. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 254–271, February, 1997.