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Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme
- Source :
-
Mathematics & Computers in Simulation . May2005, Vol. 68 Issue 4, p355-373. 19p. - Publication Year :
- 2005
-
Abstract
- 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. [Copyright &y& Elsevier]
- Subjects :
- *SOLITONS
*GEOMETRIC connections
*DIFFERENTIAL equations
*NONLINEAR theories
Subjects
Details
- Language :
- English
- ISSN :
- 03784754
- Volume :
- 68
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Mathematics & Computers in Simulation
- Publication Type :
- Periodical
- Accession number :
- 17811634
- Full Text :
- https://doi.org/10.1016/j.matcom.2005.02.017