Perturbation theory for the nonlinear Schrödinger equation with a random potential

Nonlinearity ◽

10.1088/0951-7715/22/12/004 ◽

2009 ◽

Vol 22 (12) ◽

pp. 2861-2887 ◽

Author(s):

Shmuel Fishman ◽

Yevgeny Krivolapov ◽

Avy Soffer

Keyword(s):

Perturbation Theory ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Random Potential ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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A soliton perturbation theory for the unstable nonlinear Schrödinger equation with corrections

Acta Physica Sinica (Overseas Edition) ◽

10.1088/1004-423x/8/2/005 ◽

1999 ◽

Vol 8 (2) ◽

pp. 118-130 ◽

Author(s):

Chen Zhi-de ◽

Chen Xiang-jun ◽

Huang Nian-ning

Keyword(s):

Perturbation Theory ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Soliton Perturbation

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Normalization corrections to perturbation theory for the time-independent nonlinear Schrödinger equation

Physical Review A ◽

10.1103/physreva.44.2188 ◽

1991 ◽

Vol 44 (3) ◽

pp. 2188-2191 ◽

Author(s):

János G. Ángyán ◽

Péter R. Surján

Keyword(s):

Perturbation Theory ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Direct perturbation theory for solitons of the derivative nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation

Physical Review E ◽

10.1103/physreve.65.066608 ◽

2002 ◽

Vol 65 (6) ◽

Author(s):

Xiang-Jun Chen ◽

Jianke Yang

Keyword(s):

Perturbation Theory ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Direct Perturbation ◽

Derivative Nonlinear Schrödinger Equation

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Direct perturbation theory for the dark soliton solution to the nonlinear Schrödinger equation with normal dispersion

Physical Review E ◽

10.1103/physreve.75.046604 ◽

2007 ◽

Vol 75 (4) ◽

Author(s):

Jia-Lu Yu ◽

Chun-Nuan Yang ◽

Hao Cai ◽

Nian-Ning Huang

Keyword(s):

Perturbation Theory ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Soliton Solution ◽

Schrodinger Equation ◽

Dark Soliton ◽

Nonlinear Schrodinger Equation ◽

Normal Dispersion ◽

Nonlinear Schrödinger ◽

Direct Perturbation

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The nonlinear Schrödinger equation with a random potential: results and puzzles

Nonlinearity ◽

10.1088/0951-7715/25/4/r53 ◽

2012 ◽

Vol 25 (4) ◽

pp. R53-R72 ◽

Author(s):

Shmuel Fishman ◽

Yevgeny Krivolapov ◽

Avy Soffer

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Random Potential ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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N-soliton solutions and perturbation theory for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/40/23/008 ◽

2007 ◽

Vol 40 (23) ◽

pp. 6119-6132 ◽

Author(s):

V M Lashkin

Keyword(s):

Perturbation Theory ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation

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On the Problem of Dynamical Localization in the Nonlinear Schrödinger Equation with a Random Potential

Journal of Statistical Physics ◽

10.1007/s10955-007-9472-0 ◽

2008 ◽

Vol 131 (5) ◽

pp. 843-865 ◽

Author(s):

Shmuel Fishman ◽

Yevgeny Krivolapov ◽

Avy Soffer

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Random Potential ◽

Nonlinear Schrodinger Equation ◽

Dynamical Localization ◽

Nonlinear Schrödinger

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Double-humped states in the nonlinear Schrödinger equation with a random potential

Physical Review E ◽

10.1103/physreve.81.017201 ◽

2010 ◽

Vol 81 (1) ◽

Author(s):

H. Veksler ◽

Y. Krivolapov ◽

S. Fishman

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Random Potential ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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A perturbation theory for the modified nonlinear Schrödinger equation with corrections

Physics Letters A ◽

10.1016/0375-9601(91)90540-o ◽

1991 ◽

Vol 161 (1) ◽

pp. 35-40

Author(s):

Zong-Yun Chen ◽

Nian-Ning Huang ◽

Guo-Jun Liao

Keyword(s):

Perturbation Theory ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Nonlinear Schrödinger equation with a random potential

Illinois Journal of Mathematics ◽

10.1215/ijm/1258059474 ◽

2006 ◽

Vol 50 (1-4) ◽

pp. 183-188 ◽

Author(s):

Jean Bourgain

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Random Potential ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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