The window Josephson junction: a coupled linear nonlinear system |
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| Institution: | 1. Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany;2. Laboratoire de Mathématique, INSA de Rouen, B.P. 8, 76131 Mont-Saint-Aignan Cedex, France;3. Department of Physics, University of Crete, GR-71409 Heraklion, Greece;1. Department of Materials Science and Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501, Japan;2. Research Center for Structural Materials, National Institute for Materials Science, 1-2-1, Sengen, Tsukuba, 305-0047, Japan;3. Elements Strategy Initiative for Structural Materials, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501, Japan;1. The University of Danang - University of Technology and Education, Da Nang 550000, Vietnam;2. The University of Danang - University of Science and Education, Da Nang 550000, Vietnam;3. Quality Assurance and Testing Center 2, Danang 550000, Vietnam;4. The University of Danang, Campus in Kon Tum, 704 Phan Dinh Phung, Kon Tum, Vietnam;5. Department of Chemistry and Physics, La Trobe University, Victoria 3086, Australia |
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| Abstract: | We investigate the interface coupling between the two-dimensional sine-Gordon equation and the two-dimensional wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effective one-dimensional model, and using soliton perturbation theory, compute the fixed points that can trap either a kink or antikink at an interface between two sine-Gordon media. This approximate analysis is validated by comparing with the solution of the partial differential equation and describes kink motion in the one-dimensional window junction. Using this, we analyze steady-state kink motion and derive values for the average speed in the one- and two-dimensional systems. Finally, we show how geometry and the coupling parameters can destabilize kink motion. |
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