FINITE-ELEMENT APPROXIMATION TO 2-DIMENSIONAL SINE-GORDON SOLITONS

The paper presents a finite element algorithm for the numerical solution of the sine-Gordon equation in two spatial dimensions, 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. A semidiscrete Galerkin approach based on simple four-noded bilinear finite elements in combination with a generalized Newmark integration scheme is used throughout the paper and is tested in a variety of cases. Comparisons with finite difference solutions show the superior performance of the proposed algorithm leading to very accurate, numerically stable and physically consistent solitary wave solutions. The results support the confidence in the present numerical model which should be capable to treat also more complex situations involving soliton-type interactions.