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.
Displaying similar documents to “On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation.”
A Survey on Systems of Nonlinear Schrödinger Equations
Numerical study of self-focusing solutions to the Schrödinger-Debye system
Christophe Besse, Brigitte Bidégaray (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.
On the Steps of Convergence of Approximate Eigenvectors in the Rayleigh-Schrödinger Series.
B.V. Limaye, R.P. Kulkarni (1983)
Numerische Mathematik
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Positive solutions for nonlinear Schrödinger equations with deepening potential well
Zhengping Wang, Huan-Song Zhou (2009)
Journal of the European Mathematical Society
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Numerical approximation of the weakly damped nonlinear Schrödinger equation.
Ciegis, R., Pakeniene, V. (2001)
Computational Methods in Applied Mathematics
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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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Nonlinear Galerkin Methods: The Finite Elements Case.
M. Marion, R. Temam (1990)
Numerische Mathematik
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Classical Solutions of Nonlinear Schrödinger Equations.
Nakao Hayashi (1986)
Manuscripta mathematica
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Time Dependent Nonlinear Schrödinger Equations.
Wolf von Wahl, Hartmut Pecher (1979)
Manuscripta mathematica
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Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.
Nakao Hayashi, Masayoshi Tsutsumi (1981)
Mathematische Zeitschrift
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Semiclassical states for weakly coupled nonlinear Schrödinger systems
Eugenio Montefusco, Benedetta Pellacci, Marco Squassina (2008)
Journal of the European Mathematical Society
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We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
The Cauchy problem for the nonlinear Schrödinger Equation in H1.
Thierry Cazenave, Fred B. Weissler (1988)
Manuscripta mathematica
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