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On time evolutions associated with the nonstationary Schro”dinger equation” in L

by A. K. Pogrebkov - D. Faddeev’s Seminar on Mathematical Physics, Ed. M. Semenov-Tian-Shansky, Amer. Math. Soc. Transl , 2000
"... The set of integrable symmetries of the nonstationary Schrödinger equation is shown to admit a natural decomposition into subsets of mutually commuting symmetries. Hierarchies of time evolutions associated with each of these subsets ultimately lead to nonlinear (possibly, operator) equations of the ..."
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The set of integrable symmetries of the nonstationary Schrödinger equation is shown to admit a natural decomposition into subsets of mutually commuting symmetries. Hierarchies of time evolutions associated with each of these subsets ultimately lead to nonlinear (possibly, operator) equations

Renormalized Perturbation Theory for Quartic Anharmonic Oscillator

by J. Zamastil, J. Cizek, L. Skala , 1999
"... this paper, we investigate the Schro# dinger equation for the anharmonic oscillator ..."
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this paper, we investigate the Schro# dinger equation for the anharmonic oscillator

On the Derivation of the Time-Dependent Equation of Schro dinger

by John S. Briggs, Jan M. Rost , 2000
"... Few have done more than Martin Gutzwiller to clarify the connection between classical time-dependent motion and the time-independent states of quantum systems. Hence it seems appropriate to include the following discussion of the origins of the time-dependent Schro dinger equation in this volume de ..."
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Few have done more than Martin Gutzwiller to clarify the connection between classical time-dependent motion and the time-independent states of quantum systems. Hence it seems appropriate to include the following discussion of the origins of the time-dependent Schro dinger equation in this volume

Copyright © 2011 SciRes. AM Orbital Stability of Solitary Waves for Generalized Klein-Gordon-Schrödinger Equations

by Wenhui Qi, Guoguang Lin , 2011
"... This paper concerns the orbital stability for exact solitary waves of the Generalized Klein-Gordon-Schrö-dinger equations. Since the abstract results of Grillakis et al. [1,2] can not be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain th ..."
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This paper concerns the orbital stability for exact solitary waves of the Generalized Klein-Gordon-Schrö-dinger equations. Since the abstract results of Grillakis et al. [1,2] can not be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain

Generalized Darboux Transformation and Rational Solutions for the Nonlocal Nonlinear Schrödinger Equation with the Self-Induced Parity-Time Symmetric Potential

by Jian Chen
"... In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrö-dinger equation with the self-induced parity-time symmetric potential. The N-order rational solu-tion is derived by the iterative rule and it can be expressed by the determinant form. In particular, I ca ..."
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In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrö-dinger equation with the self-induced parity-time symmetric potential. The N-order rational solu-tion is derived by the iterative rule and it can be expressed by the determinant form. In particular, I

msp STRICHARTZ ESTIMATES ON ASYMPTOTICALLY HYPERBOLIC MANIFOLDS

by Jean-marc Bouclet
"... We prove local in time Strichartz estimates without loss for the restriction of the solution of the Schrö-dinger equation, outside a large compact set, on a class of asymptotically hyperbolic manifolds. 1. The results 1 2. The strategy of the proof of Theorem 1.2 7 3. Estimates on the geodesic flow ..."
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We prove local in time Strichartz estimates without loss for the restriction of the solution of the Schrö-dinger equation, outside a large compact set, on a class of asymptotically hyperbolic manifolds. 1. The results 1 2. The strategy of the proof of Theorem 1.2 7 3. Estimates on the geodesic flow

Coulomb-attenuated exchange energy density functionals

by Peter M. W. Gill, Ross D. Adamson, John A. Pople Π, 1996
"... Exact and local spin density approximation (LSDA) exchange energy density functionals in the Coulomb-attenuated Schro $ dinger equation (CASE) approximation are constructed. When expressed as asymptotic series in the attenuation parameter x, their leading terms are identical. If a Gaussian basis set ..."
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Exact and local spin density approximation (LSDA) exchange energy density functionals in the Coulomb-attenuated Schro $ dinger equation (CASE) approximation are constructed. When expressed as asymptotic series in the attenuation parameter x, their leading terms are identical. If a Gaussian basis

Abstract

by Allan Greenleaf, Gunther Uhlmann , 2000
"... We consider the Dirichlet-to-Neumann map associated to the Schrö– dinger equation with a potential on a bounded domain Ω ⊂ R n,n ≥ 3. We show that the integral of the potential over a two-plane Π is determined by the values of the integral kernel of the Dirichlet-to-Neumann map on any open subset O ..."
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We consider the Dirichlet-to-Neumann map associated to the Schrö– dinger equation with a potential on a bounded domain Ω ⊂ R n,n ≥ 3. We show that the integral of the potential over a two-plane Π is determined by the values of the integral kernel of the Dirichlet-to-Neumann map on any open subset O

Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation

by M. Higuera A, J. Porter C, E. Knobloch C
"... Faraday waves are described, under appropriate conditions, by a damped nonlocal parametrically driven nonlinear Schrö-dinger equation. As the strength of the applied forcing increases this equation undergoes a sequence of transitions to chaotic dynamics. The origin of these transitions is explained ..."
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Faraday waves are described, under appropriate conditions, by a damped nonlocal parametrically driven nonlinear Schrö-dinger equation. As the strength of the applied forcing increases this equation undergoes a sequence of transitions to chaotic dynamics. The origin of these transitions is explained

Physica B 296 (2001) 107}111 SchroK dinger equation with imaginary potential

by Xiaozheng Ma, Costas M. Soukoulis
"... We numerically investigate the solution of the SchroK dinger equation in a one-dimensional system with gain. The gain is introduced by adding a positive imaginary potential in the system. We "nd that the time-independent solution gives that the ampli"cation suppresses wave transmission at ..."
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We numerically investigate the solution of the SchroK dinger equation in a one-dimensional system with gain. The gain is introduced by adding a positive imaginary potential in the system. We "nd that the time-independent solution gives that the ampli"cation suppresses wave transmission
Results 1 - 10 of 135