K-dV Soliton in Inhomogeneous System

Abstract

The propagation of a soliton in an inhomogeneous medium is investigated numerically by the following K-dV type equation;
u_t+6uu_x+u_xxx+c(t)u=0.
The inhomogeneous coefficient c(t) is assumed to be zero except for the period, 0≤t≤T. When the integral of c(t) from t=0 to t=T is negative, a soliton grows and generates small solitons. In the case where the integral is positive, a soliton diminishes and does not produce new soliton. In either case, the solution depends on the ratio of the distance that an initial soliton is propagated in the period 0≤t≤T to the width of the soliton.