Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme

Q. Sheng, A.Q. M. Khaliq and D.A. Voss

Mathematics and Computers in Simulation (MATCOM), 2005, vol. 68, issue 4, 355-373

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.

Keywords: Sine-Gordon equation; Solitons; Cosine scheme; Sequential splitting; Linear stability (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:68:y:2005:i:4:p:355-373

DOI: 10.1016/j.matcom.2005.02.017

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