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On time evolutions associated with the nonstationary Schro”dinger equation” in L
 D. Faddeev’s Seminar on Mathematical Physics, Ed. M. SemenovTianShansky, 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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Cited by 2 (2 self)
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of the Kadomtsev– Petviashvili I type or its higher analogues, thus demonstrating that the linear problem itself constructively determines the associated nonlinear integrable evolution equations and their hierarchies.
On the Derivation of the TimeDependent Equation of Schro dinger
, 2000
"... Few have done more than Martin Gutzwiller to clarify the connection between classical timedependent motion and the timeindependent states of quantum systems. Hence it seems appropriate to include the following discussion of the origins of the timedependent Schro dinger equation in this volume de ..."
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Few have done more than Martin Gutzwiller to clarify the connection between classical timedependent motion and the timeindependent states of quantum systems. Hence it seems appropriate to include the following discussion of the origins of the timedependent Schro dinger equation in this volume
Some inverse spectral results for semiclassical Schrödinger operators
"... Abstract. We consider a semiclassical Schrödinger operator, − � 2 ∆+ V (x). Assuming that the potential admits a unique global minimum and that the eigenvalues of the Hessian are linearly independent over Q, we show that the lowlying eigenvalues of the operator determine the Taylor series of the p ..."
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Cited by 24 (5 self)
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Abstract. We consider a semiclassical Schrödinger operator, − � 2 ∆+ V (x). Assuming that the potential admits a unique global minimum and that the eigenvalues of the Hessian are linearly independent over Q, we show that the lowlying eigenvalues of the operator determine the Taylor series
Physica B 296 (2001) 107}111 SchroK dinger equation with imaginary potential
"... We numerically investigate the solution of the SchroK dinger equation in a onedimensional system with gain. The gain is introduced by adding a positive imaginary potential in the system. We "nd that the timeindependent 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 onedimensional system with gain. The gain is introduced by adding a positive imaginary potential in the system. We "nd that the timeindependent solution gives that the ampli"cation suppresses wave transmission
Renormalized Perturbation Theory for Quartic Anharmonic Oscillator
, 1999
"... this paper, we investigate the Schro# dinger equation for the anharmonic oscillator ..."
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Cited by 2 (0 self)
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this paper, we investigate the Schro# dinger equation for the anharmonic oscillator
Stability and oscillations of twodimensional solitons described by the perturbed nonlinear Schrödinger equation
"... Abstract A perturbation theory for determining the stability characteristics of spatial optical solitons with a 2D transverse profile in a transparent medium with a weak saturation of nonlinear refractive index is developed. For Kerr nonlinearity, a new solution of linearized equations for weak so ..."
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Abstract A perturbation theory for determining the stability characteristics of spatial optical solitons with a 2D transverse profile in a transparent medium with a weak saturation of nonlinear refractive index is developed. For Kerr nonlinearity, a new solution of linearized equations for weak
The Schrödinger–Newton equation and its foundations
, 2014
"... The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semiclassical theory of gravity, in the weakfield nonrelativistic limit. We show that, while in the former case the Schröd ..."
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function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrödinger–Newton equation. 1
Coupled nonlinear Schrödinger equations arising in the study of monomode stepindex optical fibers
, 1989
"... Résumé L'équation de Schro'dinger cubique est l'équation habituelle qui régit les fluctuations de l'amplitude d'un signal dans les systèmes à faible dispersion et non linéarité cubique. Elle apparaît donc fréquement dans le domaine des fibres optiques. Cependant, dans les g ..."
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Cited by 4 (0 self)
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Résumé L'équation de Schro'dinger cubique est l'équation habituelle qui régit les fluctuations de l'amplitude d'un signal dans les systèmes à faible dispersion et non linéarité cubique. Elle apparaît donc fréquement dans le domaine des fibres optiques. Cependant, dans les
A Quantum Mechanical Supertask
 Foundations of Physics
, 1999
"... That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential SchroÈ dinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be ..."
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Cited by 19 (2 self)
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That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential SchroÈ dinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can
On the Numerical Solution of Nonlinear Schrödinger Type Equations in Fiber Optics
, 2002
"... The aim of this paper is to develop fast methods for the solution of nonlinear Schro¨dinger type equations in fiber optics. Using the method of lines we have to solve a stiff system of ordinary differential equations where the eigenvalues of the Jacobian are close to the imaginary axis. This is usu ..."
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The aim of this paper is to develop fast methods for the solution of nonlinear Schro¨dinger type equations in fiber optics. Using the method of lines we have to solve a stiff system of ordinary differential equations where the eigenvalues of the Jacobian are close to the imaginary axis
Results 1  10
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