Variable-coefficient unstable nonlinear Schrödinger equation modeling electron beam plasma: Auto-Bäcklund transformation, soliton-typed and other analytical solutions

Yi-Tian Gao; Bo Tian

doi:10.1063/1.1324656

Variable-coefficient unstable nonlinear Schrödinger equation modeling electron beam plasma: Auto-Bäcklund transformation, soliton-typed and other analytical solutions

Physics of Plasmas ◽

10.1063/1.1324656 ◽

2001 ◽

Vol 8 (1) ◽

pp. 67-73 ◽

Cited By ~ 20

Author(s):

Yi-Tian Gao ◽

Bo Tian

Keyword(s):

Electron Beam ◽

Analytical Solutions ◽

Variable Coefficient ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Nonlinear Schrodinger Equation ◽

Equation Modeling ◽

Backlund Transformation ◽

Beam Plasma ◽

Electron Beam Plasma

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Bäcklund transformations and Painlevé analysis: Exact soliton solutions for the unstable nonlinear Schrödinger equation modeling electron beam plasma

Physics of Plasmas ◽

10.1063/1.872723 ◽

1998 ◽

Vol 5 (2) ◽

pp. 395-400 ◽

Cited By ~ 19

Author(s):

A. H. Khater ◽

D. K. Callebaut ◽

R. S. Ibrahim

Keyword(s):

Electron Beam ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Equation Modeling ◽

Bäcklund Transformations ◽

Painlevé Analysis ◽

Beam Plasma ◽

Backlund Transformations ◽

Exact Soliton Solutions ◽

Electron Beam Plasma

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Multi-soliton solutions and a Bäcklund transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation with symbolic computation

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2007.08.028 ◽

2008 ◽

Vol 387 (1) ◽

pp. 97-107 ◽

Cited By ~ 26

Author(s):

Xiang-Hua Meng ◽

Wen-Jun Liu ◽

Hong-Wu Zhu ◽

Chun-Yi Zhang ◽

Bo Tian

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Symbolic Computation ◽

Variable Coefficient ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Soliton Solutions ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation

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Lax Pair, Improved Γ $\varGamma $ -Riccati Bäcklund Transformation and Soliton-Like Solutions to Variable-Coefficient Higher-Order Nonlinear Schrödinger Equation in Optical Fibers

Acta Applicandae Mathematicae ◽

10.1007/s10440-018-00233-1 ◽

2019 ◽

Vol 164 (1) ◽

pp. 185-192

Author(s):

Yinglin Lu ◽

Guangmei Wei ◽

Xin Liu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Optical Fibers ◽

Variable Coefficient ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Lax Pair ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation

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Backlund transformation for the non-isospectral and variable-coefficient non-linear Schrodinger equation

Journal of Physics A General Physics ◽

10.1088/0305-4470/22/5/010 ◽

1989 ◽

Vol 22 (5) ◽

pp. 441-449 ◽

Cited By ~ 7

Author(s):

Yu kun Zhena ◽

W L Chan

Keyword(s):

Schrödinger Equation ◽

Variable Coefficient ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Backlund Transformation ◽

Non Linear

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Symbolic computation on Bäcklund transformation and soliton solutions for a generalized nonlinear Schrödinger equation in inhomogeneous fibers

Physica Scripta ◽

10.1088/0031-8949/87/04/045014 ◽

2013 ◽

Vol 87 (4) ◽

pp. 045014

Author(s):

Pan Wang ◽

Bo Tian ◽

Yan Jiang ◽

Ming Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Symbolic Computation ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation ◽

Nonlinear Schrödinger ◽

Generalized Nonlinear Schrödinger Equation

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Higher Conservation Laws for the Nonlinear Schrodinger Equation through Backlund Transformation

Progress of Theoretical Physics ◽

10.1143/ptp.53.585 ◽

1975 ◽

Vol 53 (2) ◽

pp. 585-586 ◽

Cited By ~ 5

Author(s):

J. Satsuma

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation ◽

Nonlinear Schrödinger

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N-soliton solutions, Bäcklund transformation and Conservation laws for the integro-differential nonlinear Schrödinger equation from the isotropic inhomogeneous Heisenberg spin magnetic chain

Журнал вычислительной математики и математической физики ◽

10.7868/s0044466914040127 ◽

2014 ◽

Vol 54 (4) ◽

pp. 720-720

Author(s):

P. Wang ◽

B. Tian ◽

W.-J. Liu ◽

K. Sun

Keyword(s):

Schrödinger Equation ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation ◽

Heisenberg Spin ◽

Magnetic Chain

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Symbolic computation, Bäcklund transformation and analytic N-soliton-like solution for a nonlinear Schrödinger equation with nonuniformity term from certain space/laboratory plasmas

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2009.02.040 ◽

2009 ◽

Vol 356 (1) ◽

pp. 193-200 ◽

Cited By ~ 2

Author(s):

Hong-Wu Zhu ◽

Bo Tian ◽

Xiang-Hua Meng ◽

Xing Lü ◽

Zhen-Zhi Yao ◽

...

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Symbolic Computation ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation ◽

Nonlinear Schrödinger ◽

Laboratory Plasmas

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Bäcklund Transformation and N-Soliton Solution for the Generalized Nonlinear Schrödinger Equation

Annalen der Physik ◽

10.1002/andp.19874990404 ◽

1987 ◽

Vol 499 (4) ◽

pp. 261-264 ◽

Cited By ~ 3

Author(s):

H. Eichhorn

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Soliton Solution ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation ◽

Nonlinear Schrödinger ◽

Generalized Nonlinear Schrödinger Equation

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Bäcklund transformation and localized nonlinear wave solutions of the nonlocal defocusing coupled nonlinear Schrödinger equation

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2020.105626 ◽

2021 ◽

Vol 95 ◽

pp. 105626

Author(s):

Yunqing Yang ◽

Takashi Suzuki ◽

Jianyong Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Wave ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Bäcklund Transformation ◽

Nonlinear Schrodinger Equation ◽

Backlund Transformation ◽

Coupled Nonlinear Schrödinger Equation ◽

Wave Solutions ◽

Nonlinear Wave Solutions

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