UDC 519.642.2 Numerical Method for Computation of Sliding Velocities for Vortices in Nonlocal Josephson Electrodynamics E. V. Medvedeva Department of Higher Mathematics-1 National Research University of Electronic Technology 5, Passage 4806, Zelenograd, Moscow, Russia, 124498 In this paper, a model of infinite Josephson layered structure is considered. <...> The structure consists of alternating superconducting and tunnel layers and it is assumed that (i) the electrodynamics of the structure is nonlocal and (ii) the current-phase relation is presented by sum of Fourier harmonics instead of one sinusoidal harmonic for the case of the sine-Gordon equation. <...> The governing equation is a nonlocal generalization of the nonlinear Klein-Gordon equation with periodic nonlinearity that depends on external parameter of nonlocality λ. <...> The velocity of vortices (2π-kinks) in models of such kind are not arbitrary, but belong to some discrete set. <...> The results of computations are the families of 2π-kinks parametrized by λ. <...> It is observed that the 2π-kinks corresponding to different families for the same λ have nearly the same central part but differ in asymptotics of the tails. <...> The numerical algorithm has been incorporated into a program complex “Kink solutions” in MatLab environment. <...> Key words and phrases: Josephson junction, nonlocal Josephson electrodynamics, embedded solitons, sliding velocities, nonsinusoidal nonlinearity. 1. <...> Introduction In 90-es, in series of papers (see the survey [1]) it has been shown that in some situations the electrodynamics of distributed Josephson junction becomes nonlocal. <...> The basic equation to describe the vortex dynamics is no longer the sine-Gordon one, and it should be replaced by its nonlocal generalization (nonlocal sine-Gordon equation, NSGE). <...> It was found [2] that contrary to the sine-Gordon equation NSGE, does not support travelling simplest Josephson vortices (called also 2π-kinks or fluxons). <...> At the same time it describes fast 4π-, 6π- etc kinks and each of them can travel only with its own velocity that depends on its shape. <...> It was shown that the equation for vortex dynamics in this case is also NSGE. <...> In [5] it was assumed that CPR is described by two Fourier harmonics, therefore the governing equation was the nonlocal double sine-Gordon equation (NDSGE). <...> It was <...>