Soliton propagation in a system of two inductively coupled long Josephson junctions

We study by analytical and numerical methods soliton propagation in a system of two coupled sine-Gordon equations which describe a system of two inductively coupled Josephson junctions. We use perturbation theory to investigate the stability of the McCumber solutions and check the validity of our analysis by solving numerically the original system of PDEs. Numerical results, when a magnetic field is applied at the boundaries of such a system, are also reported.