An explicit numerical scheme for the Sine-Gordon equation in 2+1 dimensions

The paper presents an explicit finite-difference scheme for the numerical solution of the damped Sine-Gordon equation in two space variables, as it arises, for example, in rectangular large-area Josephson junctions. The dispersive nonlinear partial differential equation of the system allows for soliton-type solutions, an ubiquitous phenomenon in a large-variety of physical problems. The method of lines, based on fourth order rational approximants of the matrix-exponential term in a three-time level recurrence relation, is used to transform the initial-value problem associated with the Sine-Gordon equation into a second order, initial-value problem. The method is analyzed for local truncation error and stability. Numerical solutions for cases the involving known line and ring solitons from the bibliography are given. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.