Modulated harmonic wave in series connected discrete Josephson transmission line: the discrete calculus approach

Abstract: We consider the modulated harmonic wave in the discrete series connected Josephson transmission line (JTL). We formulate the approach to the modulation problems for discrete wave equations based on discrete calculus. We check up the approach by applying it to the Fermi-Pasta-Ulam-Tsingou type problem. Applying the approach to the discrete JTL, we obtain the equation describing the modulation amplitude, which turns out to be the defocusing nonlinear Schr\"odinger (NLS) equation. We compare the profile of the single soliton solution of the NLS with that of the soliton obtained in our previous publication.