Effect of Weak Dissipation on Two Soliton Solution of the KdV Equation
Abstract
Interaction of two solitons in a nonlinear dispersive and dissipative medium is investigated in terms of the Kortewegde 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.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 December 1979
 DOI:
 10.1143/JPSJ.47.2013
 Bibcode:
 1979JPSJ...47.2013T
 Keywords:

 KortewegDevries Equation;
 Solitary Waves;
 Wave Attenuation;
 Wave Dispersion;
 Wave Interaction;
 Amplitudes;
 Energy Dissipation;
 Perturbation Theory;
 Schroedinger Equation;
 Time Response;
 Physics (General)