Nonlinear Schrödinger equation, Bäcklund transformations and Painlevé transcendents

M. Boiti; F. Pempinelli

doi:10.1007/bf02739045

Nonlinear Schrödinger equation, Bäcklund transformations and Painlevé transcendents

Il Nuovo Cimento B ◽

10.1007/bf02739045 ◽

1980 ◽

Vol 59 (1) ◽

pp. 40-58 ◽

Cited By ~ 47

Author(s):

M. Boiti ◽

F. Pempinelli

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Bäcklund Transformations ◽

Painlevé Transcendents ◽

Nonlinear Schrödinger ◽

Backlund Transformations ◽

Painleve Transcendents

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Bäcklund transformations, conservation laws and lie symmetries for the generalized nonlinear Schrödinger equation

Group Theoretical Methods in Physics - Lecture Notes in Physics ◽

10.1007/3-540-10271-x_326 ◽

2007 ◽

pp. 170-173 ◽

Cited By ~ 1

Author(s):

J. Harnad ◽

P. Winternitz

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Lie Symmetries ◽

Bäcklund Transformations ◽

Nonlinear Schrödinger ◽

Backlund Transformations ◽

Generalized Nonlinear Schrödinger Equation

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Erratum to: Exact solutions for a perturbed nonlinear Schrödinger equation by using Bäcklund transformations

Nonlinear Dynamics ◽

10.1007/s11071-013-1109-z ◽

2013 ◽

Vol 74 (4) ◽

pp. 1153-1153 ◽

Cited By ~ 6

Author(s):

Hassan A. Zedan ◽

Eman Alaidarous ◽

S. Shapll

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Bäcklund Transformations ◽

Nonlinear Schrödinger ◽

Backlund Transformations

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An equivalent real form of the nonlinear Schrödinger equation and the permutability for Bäcklund transformations

Il Nuovo Cimento B ◽

10.1007/bf02721280 ◽

1981 ◽

Vol 62 (2) ◽

pp. 315-326 ◽

Cited By ~ 23

Author(s):

M. Boiti ◽

C. Laddomada ◽

F. Pempinelli

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Bäcklund Transformations ◽

Real Form ◽

Nonlinear Schrödinger ◽

Backlund Transformations

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Conservation laws, bilinear Bäcklund transformations and solitons for a nonautonomous nonlinear Schrödinger equation with external potentials

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2016.02.024 ◽

2016 ◽

Vol 39 ◽

pp. 472-480 ◽

Cited By ~ 24

Author(s):

Jun Chai ◽

Bo Tian ◽

Xi-Yang Xie ◽

Ya Sun

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Bäcklund Transformations ◽

Nonlinear Schrödinger ◽

Backlund Transformations

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Exact solutions for a perturbed nonlinear Schrödinger equation by using Bäcklund transformations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.1076 ◽

2009 ◽

Vol 32 (9) ◽

pp. 1068-1081 ◽

Cited By ~ 2

Author(s):

Hassan A. Zedan ◽

Seham Sh. Tantawy

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Bäcklund Transformations ◽

Nonlinear Schrödinger ◽

Backlund Transformations

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Exact solutions for a perturbed nonlinear Schrödinger equation by using Bäcklund transformations

Nonlinear Dynamics ◽

10.1007/s11071-013-1030-5 ◽

2013 ◽

Vol 74 (4) ◽

pp. 1145-1151 ◽

Cited By ~ 17

Author(s):

Hassan A. Zedan ◽

E. Aladrous ◽

S. Shapll

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Bäcklund Transformations ◽

Nonlinear Schrödinger ◽

Backlund Transformations

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Nonlinear Schrödinger Equation-Based Adjoint Sensitivity Analysis

2020 International Applied Computational Electromagnetics Society Symposium (ACES) ◽

10.23919/aces49320.2020.9196096 ◽

2020 ◽

Author(s):

Mahmoud M. T. Maghrabi ◽

Mohamed H. Bakr ◽

Shiva Kumar

Keyword(s):

Sensitivity Analysis ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Adjoint Sensitivity Analysis ◽

Adjoint Sensitivity ◽

Nonlinear Schrödinger

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Higher-order nonlinear Schrödinger equation in 2D case

Tohoku Mathematical Journal ◽

10.2748/tmj/1585101619 ◽

2020 ◽

Vol 72 (1) ◽

pp. 15-37

Author(s):

Nakao Hayashi ◽

Pavel I. Naumkin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Some properties of small perturbations against a stationary solution of the nonlinear Schrödinger equation

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2019.109570 ◽

2020 ◽

Vol 132 ◽

pp. 109570

Author(s):

Mikhail N. Smolyakov

Keyword(s):

Schrödinger Equation ◽

Stationary Solution ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Small Perturbations ◽

Nonlinear Schrödinger

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Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.4931710 ◽

2015 ◽

Vol 25 (10) ◽

pp. 103114 ◽

Cited By ~ 26

Author(s):

D. J. Kedziora ◽

A. Ankiewicz ◽

A. Chowdury ◽

N. Akhmediev

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Variable Coefficients ◽

Nonlinear Schrodinger Equation ◽

Time Variable ◽

Integrable Equations ◽

Nonlinear Schrödinger

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