A Refined Well-Posedness for the Fourth-Order Nonlinear Schrödinger Equation Related to the Vortex Filament

Communications in Partial Differential Equations ◽

10.1080/03605300701629385 ◽

2007 ◽

Vol 32 (10) ◽

pp. 1493-1510 ◽

Author(s):

Zhaohui Huo ◽

Yueling Jia

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Vortex Filament ◽

Well Posedness ◽

Nonlinear Schrödinger

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Sharp well-posedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2018027 ◽

2018 ◽

Vol 17 (2) ◽

pp. 487-504

Author(s):

Yuanyuan Ren ◽

◽

Yongsheng Li ◽

Wei Yan ◽

Keyword(s):

Cauchy Problem ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

The Cauchy Problem

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Well-posedness of Initial Value Problem for Fourth Order Nonlinear Schrodinger Equation

Pure and Applied Mathematics Quarterly ◽

10.4310/pamq.2012.v8.n4.a11 ◽

2012 ◽

Vol 8 (4) ◽

pp. 1047-1074 ◽

Author(s):

Wenxu Ge ◽

Yu-Zhu Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Initial Value Problem ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Initial Value ◽

Nonlinear Schrödinger

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The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament

Journal of Differential Equations ◽

10.1016/j.jde.2004.09.005 ◽

2005 ◽

Vol 214 (1) ◽

pp. 1-35 ◽

Author(s):

Zhaohui Huo ◽

Yueling Jia

Keyword(s):

Cauchy Problem ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Vortex Filament ◽

Nonlinear Schrödinger ◽

The Cauchy Problem

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Well-posedness and ill-posedness for the fourth order cubic nonlinear Schrödinger equation in negative Sobolev spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125342 ◽

2021 ◽

pp. 125342

Author(s):

Kihoon Seong

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Sobolev Spaces ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Cubic Nonlinear Schrödinger Equation ◽

Negative Sobolev Spaces

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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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Almost sure well-posedness for the periodic 3D quintic nonlinear Schrödinger equation below the energy space

Journal of the European Mathematical Society ◽

10.4171/jems/543 ◽

2015 ◽

Vol 17 (7) ◽

pp. 1687-1759 ◽

Author(s):

Andrea Nahmod ◽

Gigliola Staffilani

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Energy Space ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Quintic Nonlinear Schrödinger Equation

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Local Well-Posedness for the Nonlinear Schrödinger Equation in the Intersection of Modulation Spaces $$M_{p, q}^s({\mathbb {R}}^d) \cap M_{\infty , 1}({\mathbb {R}}^d)$$

Trends in Mathematics - Mathematics of Wave Phenomena ◽

10.1007/978-3-030-47174-3_6 ◽

2020 ◽

pp. 89-107

Author(s):

Leonid Chaichenets ◽

Dirk Hundertmark ◽

Peer Christian Kunstmann ◽

Nikolaos Pattakos

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Modulation Spaces ◽

Well Posedness ◽

Nonlinear Schrödinger

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