The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions

Journal of Nonlinear Science ◽

10.1007/s00332-020-09645-6 ◽

2020 ◽

Vol 30 (6) ◽

pp. 3089-3127

Author(s):

Guoqiang Zhang ◽

Zhenya Yan

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Double Pole ◽

Derivative Nonlinear Schrödinger Equation ◽

Nonzero Boundary ◽

Scattering Transforms

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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 Gerdjikov‐Ivanov–type derivative nonlinear Schrödinger equation: Long‐time dynamics of nonzero boundary conditions

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5698 ◽

2019 ◽

Vol 42 (14) ◽

pp. 4839-4861

Author(s):

Boling Guo ◽

Nan Liu

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Time Dynamics ◽

Long Time ◽

Derivative Nonlinear Schrödinger Equation ◽

Nonzero Boundary ◽

Long Time Dynamics

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Inverse scattering transform of an extended nonlinear Schrödinger equation with nonzero boundary conditions and its multisoliton solutions

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2020.123968 ◽

2020 ◽

Vol 487 (1) ◽

pp. 123968 ◽

Author(s):

Xiu-Bin Wang ◽

Bo Han

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Scattering Transform ◽

Nonzero Boundary ◽

Multisoliton Solutions

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Long-Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions in the Presence of a Discrete Spectrum

Communications in Mathematical Physics ◽

10.1007/s00220-021-03968-5 ◽

2021 ◽

Vol 382 (3) ◽

pp. 1495-1577

Author(s):

Gino Biondini ◽

Sitai Li ◽

Dionyssios Mantzavinos

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Discrete Spectrum ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Time Asymptotics ◽

Long Time ◽

Nonzero Boundary ◽

Long Time Asymptotics

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Riemann–Hilbert approach and $$N$$-soliton solutions of the generalized mixed nonlinear Schrödinger equation with nonzero boundary conditions

Theoretical and Mathematical Physics ◽

10.1134/s0040577921110052 ◽

2021 ◽

Vol 209 (2) ◽

pp. 1552-1578

Author(s):

DeQin Qiu ◽

Cong Lv

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Nonzero Boundary

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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 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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Conservation Laws for the Derivative Nonlinear Schrödinger Equation with Non-vanishing Boundary Conditions

Chinese Physics Letters ◽

10.1088/0256-307x/22/4/014 ◽

2005 ◽

Vol 22 (4) ◽

pp. 830-832 ◽

Author(s):

Chen Xiang-Jun ◽

Hou Li-Jie ◽

Lam Wa Kun

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Conservation Laws ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation

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