Stability of Nonuniform States in Systems Exhibiting Continuous Bifurcation
Many systems which are driven away from equilibrium by pumping or forcing show an instability of a stationary uniform state to a new stationary or travelling-wave state with broken translational symmetry. In continuous systems the loss of stability of the uniform state, which is usually associated with a destabilization of a normal mode, gives rise to a bifurcation of a whole manifold of new solutions. The task is then to select the members of this manifold according to their stability properties, and thus to find the candidates which may be physically realised. The travelling-wave case can be reduced to the stationary case by a transformation to a moving frame. In this paper, we therefore focus attention to stationary states.
KeywordsPeriodic Solution Brillouin Zone Closed Curf Uniform State Goldstone Mode
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