Modulated Traveling Waves in Nonequilibrium Systems
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Time periodic behaviour may arise in systems far from equilibrium due to an instability of a stationary state. If such systems are additionally able to produce spatial patterns a rich variety of phenomena occurs which have recently attracted experimental as well as theoretical interest. Experimental systems under consideration are the Taylor-Couette experiment with counter rotating cylinders , convection in binary fluid mixtures , as well as higher instabilities arising in the Bénard experiment . Since interesting spatio-temporal behaviour occurs already close to instability the description of the system can be formulated in terms of the synergetic concepts of order parameters and their dynamics  because other degrees of freedom of the systems are enslaved. The present paper gives an overview over theoretical results which have been obtained by an examination of the generalized Ginzburg-Landau equation which describes the behaviour of the system close to onset in terms of a suitably defined order parameter . Section II presents this generalized Ginzburg-Landau equation. Section III deals with one-dimensional traveling wave patterns and indicates a mechanism by which modulated traveling waves are generated. Section IV is devoted to two-dimensional traveling wave patterns.
KeywordsWave Train Amplitude Equation Oscillatory Instability Convective Roll Realistic Boundary Condition
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