Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection |
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| Affiliation: | 1. E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain;2. Department of Physics, University of California, Berkeley, CA 94720, USA;1. Hunan Key Laboratory for Micro-Nano Energy Materials and Devices, Xiangtan University, Xiangtan 411105, China;2. Laboratory for Quantum Engineering and Micro-Nano Energy Technology, Faculty of Materials and Optoelectronic Physics, Xiangtan University, Xiangtan 411105, China;1. Department of Geology, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA;2. Department of Plant Biology, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA;3. Department of Atmospheric Sciences, University of Hawaii at Mānoa, Honolulu, HI, 96822, USA;4. Illinois State Geological Survey, University of Illinois Urbana-Champaign, Champaign, IL, 61820, USA;1. Department of Virology, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran;2. Department of Virology, Pasteur Institute of Iran, Tehran, Iran;3. Department of Research and Development, Production and Research Complex, Pasteur Institute of Iran, Tehran, Iran;1. Department of Medical Psychology and Medical Sociology, Faculty of Medicine, Ruhr-University of Bochum, 44780 Bochum, Germany;2. Department of Cognitive Psychology, Faculty of Psychology, Ruhr-University of Bochum, 44780 Bochum, Germany;3. Clinic for Psychiatry, Social Psychiatry and Psychotherapy, Hannover Medical School, 30625 Hannover, Germany;1. Department of Gastroenterology, Hepatology and Endocrinology, Hannover Medical School, Hannover, Germany;2. German Centre for Infection Research (DZIF), Partner Site Hannover-Braunschweig, Germany;3. Helmholtz Centre for Infection Research (HZI), Braunschweig, Germany |
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| Abstract: | The dynamics of parametrically driven counterpropagating waves in a one-dimensional extended nearly conservative annular system are described by two coupled, damped, parametrically driven nonlinear Schrödinger (NLS) equations with opposite transport terms due to the group velocity, and small dispersion. The system is characterized by two length scales defined by a balance between (a) forcing and dispersion (the dispersive scale), and (b) forcing and advection at the group velocity (the transport scale). Both are large compared to the basic wavelength of the pattern. The dispersive scale plays an important role in the structure of solutions arising from secondary instabilities of frequency-locked spatially uniform standing waves (SW), and manifests itself both in traveling pulses or fronts and in extended spatio-temporal chaos, depending on the signs of the dispersion coefficient and nonlinearity. |
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