Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case

Journal of Differential Equations ◽

10.1016/j.jde.2016.07.026 ◽

2016 ◽

Vol 261 (9) ◽

pp. 5144-5179 ◽

Author(s):

Nakao Hayashi ◽

Jesus A. Mendez-Navarro ◽

Pavel I. Naumkin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Critical Case ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Global existence and asymptotic behavior of solutions to the fourth-order nonlinear Schrödinger equation in the critical case

Nonlinear Analysis ◽

10.1016/j.na.2014.12.024 ◽

2015 ◽

Vol 116 ◽

pp. 112-131 ◽

Author(s):

Nakao Hayashi ◽

Pavel I. Naumkin

Keyword(s):

Asymptotic Behavior ◽

Global Existence ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Critical Case ◽

Nonlinear Schrodinger Equation ◽

Asymptotic Behavior Of Solutions ◽

Nonlinear Schrödinger

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On the inhomogeneous fourth-order nonlinear Schrödinger equation

Journal of Mathematical Physics ◽

10.1063/1.4929657 ◽

2015 ◽

Vol 56 (9) ◽

pp. 093502 ◽

Author(s):

Nakao Hayashi ◽

Pavel I. Naumkin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Stability of one and two-dimensional spatial solitons in a cubic-quintic-septimal nonlinear Schrödinger equation with fourth-order diffraction and PT-symmetric potentials

Wave Motion ◽

10.1016/j.wavemoti.2021.102810 ◽

2021 ◽

pp. 102810

Author(s):

Boubakary Abdou ◽

Fabien II Ndzana ◽

Latchio Tiofack Gaston ◽

Alidou Mohamadou

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Spatial Solitons ◽

Nonlinear Schrödinger ◽

Order Diffraction

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Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces

Journal of Functional Analysis ◽

10.1016/j.jfa.2021.109150 ◽

2021 ◽

pp. 109150

Author(s):

Tadahiro Oh ◽

Kihoon Seong

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Sobolev Spaces ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Gaussian Measures ◽

Nonlinear Schrödinger ◽

Negative Sobolev Spaces

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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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Higher-order derivative nonlinear Schrödinger equation in the critical case

Journal of Mathematical Physics ◽

10.1063/1.5008500 ◽

2018 ◽

Vol 59 (2) ◽

pp. 021506

Author(s):

Pavel I. Naumkin ◽

Jhon J. Perez

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Critical Case ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Order Derivative ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation ◽

Higher Order Derivative

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A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.11.005 ◽

2021 ◽

Author(s):

Labidi Samira ◽

Khaled Omrani

Keyword(s):

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Transformation of soliton states for a (2+1) dimensional fourth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain

Laser Physics ◽

10.1088/1555-6611/aaffc9 ◽

2019 ◽

Vol 29 (3) ◽

pp. 035401 ◽

Author(s):

Chunyu Yang ◽

Abdul Majid Wazwaz ◽

Qin Zhou ◽

Wenjun Liu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Heisenberg Ferromagnetic Spin Chain

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Solitons of the fourth order nonlinear Schrödinger equation (Physics Letters A 193 (1994) 355)

Physics Letters A ◽

10.1016/0375-9601(95)00007-p ◽

1995 ◽

Vol 198 (5-6) ◽

pp. 469 ◽

Author(s):

V.I. Karpman

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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New types of exact solutions for the fourth-order dispersive cubic–quintic nonlinear Schrödinger equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.12.008 ◽

2011 ◽

Vol 217 (12) ◽

pp. 5967-5971 ◽

Author(s):

Gui-Qiong Xu

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Quintic Nonlinear Schrödinger Equation

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