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The dynamics of spatiotemporal modulations.
1Benjamin Levich Institute for Physico-Chemical Hydrodynamics and Mechanical Engineering Department, The City College of the City University of New York, New York, New York 10031Centre National de la Recherche Scientifique, Centre de Physique Theorique (Laboratoire Propre du CNRS), Luminy, CNRS, Case 907, 13288 Marseille, France.
Chaos (Woodbury, N.Y.)
|September 1, 1995
Summary
Spatiotemporal modulations can deform or break space-time symmetries in traveling waves, impacting the transition to turbulence. The study analyzes these effects using operator theory, revealing impacts on wave properties and symmetry persistence.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Fluid Dynamics
Background:
- Modulational instability of traveling waves is key to space-time disorder and turbulence.
- Understanding spatiotemporal modulations is crucial for analyzing complex dynamics.
Purpose of the Study:
- To investigate the effect of spatiotemporal modulations on dynamics.
- To compare modulated dynamics g(1)(x)g(2)(t)u(0)(x,t) with reference dynamics u(0)(x,t).
Main Methods:
- Operator theory is used to analyze the properties of modulated dynamics.
- Comparison of symmetries and dimensional properties of modulated versus reference dynamics.
Main Results:
- Modulations deform or break space-time symmetries based on operator unitarity.
- The dimension of the Euclidean space for modulated dynamics is reduced or maintained.
- Spatiotemporal translation invariance is lost with modulation.
- Symmetry persistence depends on Fourier sideband resonance.
Conclusions:
- Modulated waves exhibit altered symmetries compared to carrier waves.
- Nonresonant cases allow for explicit determination of spatiotemporal symmetry.
- Modulated waves share spectra and entropy with carrier waves, with correlations affected by modulation.