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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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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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, 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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Complete symmetry reductions, conservation laws and exact solutions for a (2 + 1)-dimensional nonlinear Schrödinger equation

Optik ◽

10.1016/j.ijleo.2021.166504 ◽

2021 ◽

Vol 232 ◽

pp. 166504

Author(s):

Hongyan Zhi

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Symmetry Reductions ◽

Complete Symmetry

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Kinetic and thermodynamical interpretation of the conservation laws of a nonlinear Schrödinger equation and other completely integrable systems

Il Nuovo Cimento B ◽

10.1007/bf02721517 ◽

1985 ◽

Vol 85 (1) ◽

pp. 1-16 ◽

Cited By ~ 3

Author(s):

T. A. Minelli ◽

A. Pascolini

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Integrable Systems ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Completely Integrable Systems ◽

Nonlinear Schrödinger ◽

Completely Integrable

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Soliton Solutions and Conservation Laws for an Inhomogeneous Fourth-Order Nonlinear Schrödinger Equation

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542518110106 ◽

2018 ◽

Vol 58 (11) ◽

pp. 1856-1864

Author(s):

Pan Wang ◽

Feng-Hua Qi ◽

Jian-Rong Yang

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Conservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2011.12.009 ◽

2012 ◽

Vol 17 (8) ◽

pp. 3247-3257 ◽

Cited By ~ 19

Author(s):

Shou-Fu Tian ◽

Li Zou ◽

Qi Ding ◽

Hong-Qing Zhang

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Modulational Instability ◽

Nonlinear Schrodinger Equation ◽

Time Dependent ◽

Matter Wave ◽

Nonlinear Schrödinger

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

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

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

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

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

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

Nonlinear Schrödinger equation, Bäcklund transformations and Painlevé transcendents

Complete symmetry reductions, conservation laws and exact solutions for a (2 + 1)-dimensional nonlinear Schrödinger equation

Kinetic and thermodynamical interpretation of the conservation laws of a nonlinear Schrödinger equation and other completely integrable systems

Soliton Solutions and Conservation Laws for an Inhomogeneous Fourth-Order Nonlinear Schrödinger Equation

Conservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity

Complete symmetry reductions, conservation laws and exact solutions for a (2 + 1)-dimensional nonlinear Schrödinger equation