A Survey on Systems of Nonlinear Schrödinger Equations
Antonio Ambrosetti (2008)
Bollettino dell'Unione Matematica Italiana
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We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
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A Survey on Systems of Nonlinear Schrödinger Equations
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The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces
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Journal of the European Mathematical Society
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Ramona Anton (2008)
Bulletin de la Société Mathématique de France
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We prove wellposedness of the Cauchy problem for the nonlinear Schrödinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on manifolds with Lipschitz metric.