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On a smooth, closed Riemannian manifold, we study the question ofproportionality of components, also called synchronization, of vector-valuedsolutions to nonlinear elliptic Schr\"odinger systems with constantcoefficients. In particular, we obtain bifurcation results showing theexistence of branches of non-synchronized solutions emanating from the constantsolutions.

Non-synchronized solutions to nonlinear elliptic Schr\"odinger systems on a closed Riemannian manifold