Asymptotic states in long Josephson junctions in an external magnetic field.

Asymptotic states in long Josephson junctions are investigated in an external magnetic field. We show that a choice one of the solution of the stationary Ferrell-Prange equation can carry be out with use of an asymptotic solution of the sine-Gordon equation and that an evolution to that stable solution occurs by passing through metastable states, which is determined with a form of quickly damped initial perturbation. The boundary sine-Gordon and Ferrell-Prange problems were carried out with a numerical simulation. An approximated expression for the vortex and antivortex states is obtained in the case of large values of an external magnetic field. The problem of magnetic field penetration in long Josephson junctions is in a sense a classical one [1]–[5]. Nevertheless, interest in it has not abated [6]–[13]. For example, in long Josephson junctions a dynamical chaos was discovered [6]–[10]. A long Josephson junction is a very good system to study Josephson vortex (fluxons, solitons) motions and vortex interactions [12]–[13]. It is well known that a weak magnetic field penetrates exponentially in a long Josephson junction. In a strong magnetic field a state of the long Josephson junction arises that is characterized by the appearance of a Josephson vortex. An equation that describes this phenomenon is nonlinear and in a general case it is the driven damped sine-Gordon equation. In a stationary case we have the nonlinear Ferrell-Prange equation and one would think