Coherence and chaos in the driven damped sine-gordon equation: Measurement of the soliton spectrum |
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| Affiliation: | 1. Department of Mathematical Sciences, Shahrekord University, Shahrekord, Iran;2. Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam;3. Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam;1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;2. Shen Yuan Honors College, Beijing University of Aeronautics and Astronautics, Beijing 100191, China |
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| Abstract: | A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field (φ, φt) which is periodic in space. The procedure is applied to the field generated by a damped, driven sine-Gordon equation. This field can be either temporally periodic (locked to the driver) or chaotic. In either case the numerical measurement shows that the spatial structure can be described by only a few spatially localized (soliton wave-train) modes. The numerical procedure quantitatively identifies the presence, number and properties of these soliton wave-trains. For example, an increase of spatial symmetry is accompanied by the injection of additional solitons into the field. |
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