Soliton and Generation of Tail in Nonlinear Dispersive Media with Weak Dissipation

Abstract

Propagation of a soliton and generation of a tail by the soliton are investigated analytically and numerically for Korteweg-de Vries equation with dissipation term. The analytical solution obtained by the modified conservation laws shows that the amplitude and velocity of a soliton change in time due to the dissipation. At the same time, a non-soliton part—a tail—appears in the solution. The structure of a tail depends on the dissipation term. Numerical solutions confirm qualitatively the validity of the analytical solution. An overtaking collision of two solitons is also examined numerically.