Analytical Solutions of Traveling Fluxon Waves on a Josephson Transmission Line with Shunt Conductance and Uniform Bias Current

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Abstract
Traveling-wave type solutions describing the fluxon motion on an infinite Josephson transmission line with shunt conductance and uniform bias current are derived analytically by approximating the sinusoidal current vs. phase-difference relation of the Josephson junction by a triangular saw-tooth like relation. From the result, the relation between the velocity of the waves and the bias current is obtained numerically, and the dependence of the phase and voltage upon space and time is also obtained. Finally, the energy flow of the waves along the line is expressed by a simple formula.