Travelling Waves on a Josephson Transmission Line

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Abstract
Various properties of stationary travelling waves propagating along a Josephson transmission line having positive nonlinear differential tunnelling conductance and distributed bias current are discussed geometrically in the state plane. First, the change of patterns of solutions in the state plane is uniquely determined for changes in conductance, fluxon velocity and bias current. Second, it is demonstrated that for the linear component of the conductance only, an event takes place in which the solitary wave velocity does not reach the velocity of the electromagnetic waves on a dissipationless transmission line in the certain limit of bias current. Finally, it is shown numerically that the non-linearity of the conductance has important effects on the waves, both quantitatively and qualitatively.