Kinks and rotations in long Josephson junctions

Kinks and rotations are studied in long Josephson junctions for small and l arge surface losses. Geometric singular perturbation theory is used to prov e existence for small surface losses, while numerical continuation is neces sary to handle large surface losses. A survey of the system behaviour in te rms of dissipation parameters and bias current is given. Linear orbital sta bility for kinks is proved for small surface losses by calculating the spec trum of the linearized problem. The spectrum is split into essential spectr um and discrete spectrum. For the determination of the discrete spectrum, r obustness of exponential dichotomies is used. Puiseux series together with perturbation theory for linear operators are an essential tool. In a final step, a smooth Evans function together with geometric singular perturbation theory is used to count eigenvalues. For kinks, non-linear orbital stabili ty is shown. For this purpose, the asymptotic behaviour of a semigroup is g iven and the theory of centre and stable manifolds is applied. Copyright (C ) 2001 John Wiley & Sons, Ltd.