Lower bounds on the growth of Sobolev norms in some linear time dependent Schrödinger equations

Mathematical Research Letters ◽

10.4310/mrl.2019.v26.n4.a11 ◽

2019 ◽

Vol 26 (4) ◽

pp. 1197-1215 ◽

Author(s):

Alberto Maspero

Keyword(s):

Lower Bounds ◽

Linear Time ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

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On growth of Sobolev norms in time dependent linear Schrödinger equations on spheres

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.01.029 ◽

2012 ◽

Vol 390 (1) ◽

pp. 165-180

Author(s):

Qidi Zhang ◽

Daoyuan Fang

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

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Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential

Global Solutions of Nonlinear Schrödinger Equations - Colloquium Publications ◽

10.1090/coll/046/07 ◽

1999 ◽

pp. 155-172

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Sobolev Norms ◽

Dependent Potential

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On Growth of Sobolev Norms in Linear Schrödinger Equations with Time Dependent Gevrey Potential

Journal of Dynamics and Differential Equations ◽

10.1007/s10884-012-9244-7 ◽

2012 ◽

Vol 24 (2) ◽

pp. 151-180 ◽

Author(s):

Daoyuan Fang ◽

Qidi Zhang

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

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Growth of Sobolev norms for time dependent periodic Schrödinger equations with sublinear dispersion

Journal of Differential Equations ◽

10.1016/j.jde.2018.10.017 ◽

2019 ◽

Vol 266 (8) ◽

pp. 4953-4996 ◽

Author(s):

Riccardo Montalto

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

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On time dependent Schrödinger equations: Global well-posedness and growth of Sobolev norms

Journal of Functional Analysis ◽

10.1016/j.jfa.2017.02.029 ◽

2017 ◽

Vol 273 (2) ◽

pp. 721-781 ◽

Author(s):

A. Maspero ◽

D. Robert

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

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Logarithmic Bounds on Sobolev Norms for Time Dependent Linear Schrödinger Equations

Communications in Partial Differential Equations ◽

10.1080/03605300802537115 ◽

2008 ◽

Vol 33 (12) ◽

pp. 2164-2179 ◽

Author(s):

W.-M. Wang

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

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On growth of sobolev norms in linear schrödinger equations with smooth time dependent potential

Journal d Analyse Mathématique ◽

10.1007/bf02791265 ◽

1999 ◽

Vol 77 (1) ◽

pp. 315-348 ◽

Author(s):

J. Bourgain

Keyword(s):

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Sobolev Norms ◽

Dependent Potential

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Domain decomposition method for the N-body time-independent and time-dependent Schrödinger equations

Numerical Algorithms ◽

10.1007/s11075-018-0566-3 ◽

2018 ◽

Vol 81 (2) ◽

pp. 655-694 ◽

Author(s):

Emmanuel Lorin

Keyword(s):

Domain Decomposition ◽

Decomposition Method ◽

Domain Decomposition Method ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations

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Persistent bright solitons in sign-indefinite coupled nonlinear Schrödinger equations with a time-dependent harmonic trap

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2015.06.026 ◽

2016 ◽

Vol 31 (1-3) ◽

pp. 30-39 ◽

Author(s):

R. Radha ◽

P.S. Vinayagam ◽

J.B. Sudharsan ◽

Boris A. Malomed

Keyword(s):

Harmonic Trap ◽

Nonlinear Schrödinger Equations ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Bright Solitons ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

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Higher order exponential split operator method for solving time-dependent Schrödinger equations

Canadian Journal of Chemistry ◽

10.1139/v92-078 ◽

1992 ◽

Vol 70 (2) ◽

pp. 555-559 ◽

Author(s):

André D. Bandrauk ◽

Hai Shen

Keyword(s):

Fourier Transform ◽

Fast Fourier Transform ◽

Operator Method ◽

Computation Time ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Exponential Form ◽

Operator Solution ◽

A new method of splitting exponential operators is proposed for the exponential form of the operator solution to the time-dependent Schrödinger equation. The method is shown to hold for any desired accuracy in the time increment. A comparison of different algorithms is made as a function of accuracy and computation time. Keywords: splitting operator, Fast Fourier Transform (FFT), Schrödinger equations.

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