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• W2068988900 abstract "This paper proposes a split cosine scheme for simulating solitary solutions of the sine-Gordon equation in two dimensions, as it arises, for instance, in rectangular large-area Josephson junctions. The dispersive nonlinear partial differential equation allows for soliton-type solutions, a ubiquitous phenomenon in a large variety of physical problems. The semidiscretization approach first leads to a system of second-order nonlinear ordinary differential equations. The system is then approximated by a nonlinear recurrence relation which involves a cosine function. The numerical solution of the system is obtained via a further application of a sequential splitting in a linearly implicit manner that avoids solving the nonlinear scheme at each time step and allows an efficient implementation of the simulation in a locally one-dimensional fashion. The new method has potential applications in further multi-dimensional nonlinear wave simulations. Rigorous analysis is given for the numerical stability. Numerical demonstrations for colliding circular solitons are given." @default.
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• W2068988900 date "2005-05-01" @default.
• W2068988900 modified "2023-10-16" @default.
• W2068988900 title "Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme" @default.
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• W2068988900 doi "https://doi.org/10.1016/j.matcom.2005.02.017" @default.
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