Effect of Weak Dissipation on Two Soliton Solution of the K-dV Equation

Interaction of two solitons in a nonlinear dispersive and dissipative medium is investigated in terms of the Korteweg-de Vries equation with small dissipation. A perturbation method based upon the inverse scattering transform is applied to estimate the changes in amplitudes of two interacting solitons. Differences are found in amplitude changes according to the amplitude ratio of initial solitons and to the form of the dissipation term. Theoretical predictions are ascertained by numerical experiments of corresponding initial value problem leading to a qualitatively satisfactory agreement.