Flux-flow mode in the sine-Gordon system

An inverse transformation of the theta function is derived, making it possible to investigate a multiperiodic solution of the sine-Gordon equation in the limit of a dense sequence of overlapping solitons. A special case of a unidirectional soliton train interacting with small-amplitude quasi-linear oscillations is discussed as a simple model of the flux-flow state in a long one-dimensional Josephson junction. Approximate analytical solutions for the dispersion parameters are compared with numerical results. (C) 1998 Elsevier Science B.V.