The higher-order nonlinear Schrödinger equation with non-zero boundary conditions: Robust inverse scattering transform, breathers, and rogons

Physics Letters A ◽

10.1016/j.physleta.2019.125906 ◽

2019 ◽

Vol 383 (29) ◽

pp. 125906 ◽

Author(s):

Shuyan Chen ◽

Zhenya Yan

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Higher Order ◽

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 ◽

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 discrete nonlinear Schrödinger equation with nonvanishing boundary conditions

Inverse Problems ◽

10.1088/0266-5611/23/4/021 ◽

2007 ◽

Vol 23 (4) ◽

pp. 1711-1758 ◽

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 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 ◽

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 derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

Physical Review E ◽

10.1103/physreve.69.066604 ◽

2004 ◽

Vol 69 (6) ◽

Author(s):

Xiang-Jun Chen ◽

Wa Kun Lam

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

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 nonzero boundary conditions

Journal of Mathematical Physics ◽

10.1063/1.4868483 ◽

2014 ◽

Vol 55 (3) ◽

pp. 031506 ◽

Author(s):

Gino Biondini ◽

Gregor Kovačič

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform ◽

Nonzero Boundary

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Inverse Scattering Transform for the Multi-Component Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

Studies in Applied Mathematics ◽

10.1111/j.1467-9590.2010.00504.x ◽

2011 ◽

Vol 126 (3) ◽

pp. 245-302 ◽

Author(s):

Barbara Prinari ◽

Gino Biondini ◽

A. David Trubatch

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform ◽

Nonzero Boundary

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The inverse scattering transform for the focusing nonlinear Schrödinger equation with asymmetric boundary conditions

Journal of Mathematical Physics ◽

10.1063/1.4898768 ◽

2014 ◽

Vol 55 (10) ◽

pp. 101505 ◽

Author(s):

F. Demontis ◽

B. Prinari ◽

C. van der Mee ◽

F. Vitale

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 vector nonlinear Schrödinger equation with nonvanishing boundary conditions

Journal of Mathematical Physics ◽

10.1063/1.2209169 ◽

2006 ◽

Vol 47 (6) ◽

pp. 063508 ◽

Author(s):

Barbara Prinari ◽

Mark J. Ablowitz ◽

Gino Biondini

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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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 ◽

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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