Properties of confined states in phase dynamics

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Abstract
In this paper we point out that for the confined states discussed recently for the phase associated with a stationary pattern, a conservation law for both the phase variation and the local wave vector exists. We discuss the physical implications of this observation as a function of the imposed boundary conditions. We investigate the influence of noise and we find that for the phase change and for the local wave vector, the stationary solution of the associated functional differential Fokker-Planck equation can be explicitly given.