BOUND SOLITONS IN THE AC-DRIVEN, DAMPED NONLINEAR SCHRODINGER-EQUATION

We demonstrate analytically that the effective potential of interactio n between widely separated solitons in a damped, ac-driven nonlinear S chrodinger equation is oscillatory at large distances. We show numeric ally that two solitons in the system attract each other if the initial distance between them is smaller than a certain critical value; conse quently, they will either form an oscillatory bound state with a finit e lifetime, collapse to a stable single soliton state, or decay to the rotating background. If the initial separation is greater than the cr itical value, they separate to form a stable bound state at a second c ritical distance. The critical distances are in good agreement with th e analytical prediction.