Bound states of solitons in semi-infinite Josephson junctions with microscopic inhomogeneity

Linearised non-uniform sine-Gordon equation describing the distribution of magnetic flux in the semi-infinite Josephson junction with a micro-inhomogeneity is considered. It is shown that the piecewise-linear approximation we use preserved some properties of the initial nonlinear equation. Arising stable states are analysed in detail. Part of them undergo bifurcations when the external magnetic field is changed.