On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
N. Hayashi, K. Nakamitsu, M. Tsutsumi (1986)
Mathematische Zeitschrift
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Displaying similar documents to “Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.”
On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
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We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
Time Decay for Some Schrödinger Equations.
Nakao Hayashi, Tohru Ozawa (1988/89)
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Positive solutions for nonlinear Schrödinger equations with deepening potential well
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Commutator Methods and a Smoothing Property of the Schrödinger Evolution Group.
Arne Jensen (1986)
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Classical Solutions of Nonlinear Schrödinger Equations.
Nakao Hayashi (1986)
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Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
Jean Bourgain, W. Wang (1997)
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Time Dependent Nonlinear Schrödinger Equations.
Wolf von Wahl, Hartmut Pecher (1979)
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The Cauchy problem for the nonlinear Schrödinger Equation in H1.
Thierry Cazenave, Fred B. Weissler (1988)
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Asymptotics of the Nodal Lines of Solutions of 2-Dimensional Schrödinger Equations.
M. Hoffmann-Ostenhof (1988)
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Nonlinear Schrödinger equation on four-dimensional compact manifolds
Patrick Gérard, Vittoria Pierfelice (2010)
Bulletin de la Société Mathématique de France
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We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness...