Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

Xin Zhou

doi:10.1007/bf02096873

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

Communications in Mathematical Physics ◽

10.1007/bf02096873 ◽

1990 ◽

Vol 128 (3) ◽

pp. 551-564 ◽

Cited By ~ 46

Author(s):

Xin Zhou

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Time Dependent ◽

Scattering Transform

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The inverse scattering transform for the time-dependent Schrodinger equation and Kadomtsev-Petviashvili equation

Physica D Nonlinear Phenomena ◽

10.1016/0167-2789(81)90145-7 ◽

1981 ◽

Vol 3 (1-2) ◽

pp. 420-427 ◽

Cited By ~ 145

Author(s):

S.V. Manakov

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Time Dependent ◽

Scattering Transform ◽

Petviashvili Equation

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Triple-pole soliton solutions of the derivative nonlinear Schrödinger equation via inverse scattering transform

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107741 ◽

2021 ◽

pp. 107741

Author(s):

Nan Liu ◽

Zuxing Xuan ◽

Jinyi Sun

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform ◽

Derivative Nonlinear Schrödinger Equation

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Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation with a One-Sided Non-Zero Boundary Condition

Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations - Contemporary Mathematics ◽

10.1090/conm/651/13035 ◽

2015 ◽

pp. 157-194 ◽

Cited By ~ 8

Author(s):

B. Prinari ◽

F. Vitale

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2016.04.003 ◽

2016 ◽

Vol 333 ◽

pp. 117-136 ◽

Cited By ~ 12

Author(s):

Gino Biondini ◽

Emily Fagerstrom ◽

Barbara Prinari

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

Nonlinearity ◽

10.1088/0951-7715/29/3/915 ◽

2016 ◽

Vol 29 (3) ◽

pp. 915-946 ◽

Cited By ~ 196

Author(s):

Mark J Ablowitz ◽

Ziad H Musslimani

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Nonlocal Nonlinear

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Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions

Inverse Problems ◽

10.1088/0266-5611/23/4/021 ◽

2007 ◽

Vol 23 (4) ◽

pp. 1711-1758 ◽

Cited By ~ 39

Author(s):

Mark J Ablowitz ◽

Gino Biondini ◽

Barbara Prinari

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows

Studies in Applied Mathematics ◽

10.1111/sapm.12347 ◽

2020 ◽

Author(s):

Gino Biondini ◽

Jonathan Lottes ◽

Dionyssios Mantzavinos

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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Inverse Scattering Transform for the Discrete Focusing Nonlinear Schrödinger Equation with Nonvanishing Boundary Conditions

Journal of Nonlinear Mathematical Physics ◽

10.1080/14029251.2015.1023583 ◽

2015 ◽

Vol 22 (2) ◽

pp. 233-264 ◽

Cited By ~ 6

Author(s):

Cornelis van der Mee

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

Journal of Mathematical Physics ◽

10.1063/1.5018294 ◽

2018 ◽

Vol 59 (1) ◽

pp. 011501 ◽

Cited By ~ 55

Author(s):

Mark J. Ablowitz ◽

Xu-Dan Luo ◽

Ziad H. Musslimani

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Scattering Transform ◽

Nonzero Boundary ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Nonlocal Nonlinear

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Numerical inverse scattering transform for the periodic, defocusing nonlinear Schrödinger equation

Physics Letters A ◽

10.1016/0375-9601(93)90319-u ◽

1993 ◽

Vol 176 (1-2) ◽

pp. 75-84 ◽

Cited By ~ 14

Author(s):

A.R. Osborne

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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