Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model |
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| Institution: | 1. Mathematical Sciences Research, Bell Laboratories—Lucent Technologies, Murray Hill, NJ 07974, USA;2. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA;3. Department of Mechanical and Aerospace Engineering, Program in Applied and Computational Mathematics, Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA;1. Sorbonne Université, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France;2. CMLS, École Polytechnique, CNRS, 91128 Palaiseau Cedex, France;3. Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, China;1. Institute for Analysis, Karlsruhe Institute of Technology (KIT), Englerstraße 2, 76131 Karlsruhe, Germany;2. Department of Mathematics, Sogang University, 35 Baekbeom-ro, Mapo-gu, Seoul 04107, South Korea;3. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801-2975, USA |
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| Abstract: | We study a model derived by Fei et al. Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory. |
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