Local well-posedness for a system of quadratic nonlinear Schrödinger equations in one or two dimensions

Huali Zhang

doi:10.1002/mma.3863

Local well-posedness for a system of quadratic nonlinear Schrödinger equations in one or two dimensions

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.3863 ◽

2016 ◽

Vol 39 (14) ◽

pp. 4257-4267 ◽

Cited By ~ 3

Author(s):

Huali Zhang

Keyword(s):

Two Dimensions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Ill-posedness for a system of quadratic nonlinear Schrödinger equations in two dimensions

Journal of Functional Analysis ◽

10.1016/j.jfa.2016.04.017 ◽

2016 ◽

Vol 271 (1) ◽

pp. 136-163

Author(s):

Tsukasa Iwabuchi ◽

Takayoshi Ogawa ◽

Kota Uriya

Keyword(s):

Two Dimensions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Local well-posedness and smoothing effects of strongsolutions for nonlinear Schrödinger equations with potentials and magnetic fields

Hokkaido Mathematical Journal ◽

10.14492/hokmj/1285766208 ◽

2005 ◽

Vol 34 (1) ◽

pp. 37-63 ◽

Cited By ~ 4

Author(s):

Yoshihisa NAKAMURA ◽

Akihiro SHIMOMURA

Keyword(s):

Magnetic Fields ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Smoothing Effects ◽

Nonlinear Schrodinger Equations

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The well-posedness of nonlinear Schrödinger equations in Triebel-type spaces

Pacific Journal of Mathematics ◽

10.2140/pjm.2015.274.325 ◽

2015 ◽

Vol 274 (2) ◽

pp. 325-354

Author(s):

Shaolei Ru ◽

Jiecheng Chen

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Type Spaces

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Local well-posedness of the nonlinear Schrödinger equations on the sphere for data in modulation spaces

Communications in Partial Differential Equations ◽

10.1080/03605302.2015.1123274 ◽

2015 ◽

Vol 41 (4) ◽

pp. 732-747 ◽

Cited By ~ 1

Author(s):

Hideo Takaoka

Keyword(s):

Nonlinear Schrödinger Equations ◽

Modulation Spaces ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Nonlinear Schrödinger Equations with a Four-Well Potential in Two Dimensions: Bifurcations and Stability Analysis

Nonlinear Science and Complexity ◽

10.1007/978-90-481-9884-9_22 ◽

2011 ◽

pp. 173-179

Author(s):

C. Wang ◽

G. Theocharis ◽

P. G. Kevrekidis ◽

N. Whitaker ◽

D. J. Frantzeskakis ◽

...

Keyword(s):

Stability Analysis ◽

Two Dimensions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions d⩾9

Journal of Differential Equations ◽

10.1016/j.jde.2011.08.009 ◽

2011 ◽

Vol 251 (12) ◽

pp. 3381-3402 ◽

Cited By ~ 29

Author(s):

Changxing Miao ◽

Guixiang Xu ◽

Lifeng Zhao

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when $d = 2,3$ and $u_0$ is radial

Cambridge Journal of Mathematics ◽

10.4310/cjm.2019.v7.n3.a2 ◽

2019 ◽

Vol 7 (3) ◽

pp. 283-318

Author(s):

Benjamin Dodson

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2015.09.005 ◽

2016 ◽

Vol 105 (1) ◽

pp. 31-65 ◽

Cited By ~ 13

Author(s):

Michael Ruzhansky ◽

Baoxiang Wang ◽

Hua Zhang

Keyword(s):

Fourth Order ◽

Sobolev Spaces ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Small Data ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite norm

Nonlinear Analysis ◽

10.1016/j.na.2010.10.003 ◽

2011 ◽

Vol 74 (4) ◽

pp. 1304-1319 ◽

Cited By ~ 2

Author(s):

Ryosuke Hyakuna ◽

Takamasa Tanaka ◽

Masayoshi Tsutsumi

Keyword(s):

Initial Data ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Large Initial Data ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Infinite Norm

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Global well-posedness of critical nonlinear Schrödinger equations below $L^2$

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2013.33.1389 ◽

2013 ◽

Vol 33 (4) ◽

pp. 1389-1405 ◽

Cited By ~ 7

Author(s):

Yonggeun Cho ◽

◽

Gyeongha Hwang ◽

Tohru Ozawa ◽

◽

...

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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