A detailed analysis is given to the solution of the cubic Schrödinger equationiqt+qxx+ 2|q|2q= 0 under the boundary conditions as |x|→∞. The inverse‐scattering technique is used, and the asymptotic state is a series of solitons. However, there is no soliton whose amplitude is stationary in time. Each soliton has a definite velocity and “pulsates” in time with a definite period. The interaction of two solitons is considered, and a possible extension to the perturbed periodic wave [q(x+T,t) =q(x,t) as |x|→∞