Existence, Uniqueness, and Nonuniqueness of Single-Wave-Form Solutions to Josephson Junction Systems

We study the existence and uniqueness of single-wave-form solutions for series arrays of N Josephson junctions coupled through general RLC loads. Our method recasts the conditions for a single-wave-form solution as a fixed point equation on a Hilbert space. We use this technique to prove that single-wave-form solutions exist when the bias current I is greater than 1 and are essentially unique when either N or I is large. We also employ these ideas to give explicit examples of series arrays which posess several distinct single-wave-form solutions.