Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

Chengchun Hao;

doi:10.3934/cpaa.2007.6.997

Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2007.6.997 ◽

2007 ◽

Vol 6 (4) ◽

pp. 997-1021 ◽

Cited By ~ 15

Author(s):

Chengchun Hao ◽

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

One Dimensional ◽

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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One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Nonlinear Dynamics ◽

10.1007/s11071-019-05240-x ◽

2019 ◽

Vol 98 (2) ◽

pp. 985-995 ◽

Cited By ~ 10

Author(s):

Liangwei Zeng ◽

Jianhua Zeng

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Linear Potential ◽

Schrödinger Equations ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Gap Solitons

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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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Inhomogeneous Dirichlet-boundary value problem for one dimensional nonlinear Schrödinger equations via factorization techniques

Journal of Differential Equations ◽

10.1016/j.jde.2018.07.063 ◽

2019 ◽

Vol 266 (2-3) ◽

pp. 1121-1152 ◽

Cited By ~ 2

Author(s):

Liliana Esquivel ◽

Nakao Hayashi ◽

Elena I. Kaikina

Keyword(s):

Boundary Value Problem ◽

Dirichlet Boundary ◽

Boundary Value ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Dirichlet Boundary Value Problem ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Inhomogeneous Neumann-boundary value problem for one dimensional nonlinear Schrödinger equations via factorization techniques

Journal of Mathematical Physics ◽

10.1063/1.5083078 ◽

2019 ◽

Vol 60 (9) ◽

pp. 091507

Author(s):

Liliana Esquivel ◽

Nakao Hayashi ◽

Elena I. Kaikina

Keyword(s):

Boundary Value Problem ◽

Boundary Value ◽

Neumann Boundary ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Neumann Boundary Value Problem ◽

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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