Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8567Research ArticleNumerical Method for Computation of Sliding Velocities for Vortices in Nonlocal Josephson ElectrodynamicsMedvedevaE VDepartment of Higher Mathematics-1elinamedvedeva87@gmail.comNational Research University of Electronic Technology150120151455208092016Copyright © 2015,2015In 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 (2 π-kinks) in models of such kind are not arbitrary, but belong to some discrete set. The paper presents a method for computation of these velocities (called also “sliding velocities”) and the shapes of kinks. The estimation of error of the method is given. The results of computations are the families of 2 π-kinks parametrized by λ. It is observed that the 2 π-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. The complex enables to compute the shapes and velocities of 2 π-kinks for nonlinearities represented by sums of up to ten Fourier harmonics, as well as to model the propagation of these kinks.Josephson junctionnonlocal Josephson electrodynamicsembedded solitonssliding velocitiesnonsinusoidal nonlinearityджозефсоновский переходнелокальная джозефсоновская электродинамикавложенные солитоныскорости скольжениянесинусоидальная нелинейность