  A long Josephson junction in a constant external magnetic field and in the
presence of a dc bias current is investigated. It is shown that the system,
simulated by the sine-Gorgon equation, "remembers" a rapidly damping initial
perturbation and final asymptotic states are determined exactly with this
perturbation. Numerical solving of the boundary sine-Gordon problem and
calculations of Lyapunov indices show that this system has a memory even when
it is in a state of dynamical chaos, i.e., dynamical chaos does not destroy
initial information having a character of rapidly damping perturbation.
