Moving embedded solitons in the discrete double sine-Gordon equation

Abstract

The soliton mobility in the discrete double sine-Gordon (DDbSG) equation is investigated. This equation is used as a model of various physical applications, including the arrays of small Josephson junctions. In particular, it describes the array of asymmetric three-junction superconducting quantum interference devices (SQUIDs) with one junction in one arm of the SQUID and two junctions in another arm of it. The DDbSG equation is investigated both in the hamiltonian limit and in the presence of dissipation and dc bias. The existence of perfectly localized embedded solitons that can propagate with some selected values of velocity has been demonstrated numerically with the help of the pseudo-spectral method. The embedded soliton existence diagram is constructed on the parameter plane. The signatures of the embedded solitons on the current-voltage curves of the array are discussed.