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Almost cubic nonlinear Schrödinger equation: Existence, uniqueness and scattering
1.  Department of Mathematics, Bogaziçi University, Bebek 34342, Istanbul, Turkey, Turkey 
[1] 
Uchida Hidetake. Analytic smoothing effect and global existence of small solutions for the elliptichyperbolic DaveyStewartson system. Conference Publications, 2001, 2001 (Special) : 182190. doi: 10.3934/proc.2001.2001.182 
[2] 
Shiming Li, Yongsheng Li, Wei Yan. A global existence and blowup threshold for DaveyStewartson equations in $\mathbb{R}^3$. Discrete & Continuous Dynamical Systems  S, 2016, 9 (6) : 18991912. doi: 10.3934/dcdss.2016077 
[3] 
Jing Lu, Yifei Wu. Sharp threshold for scattering of a generalized DaveyStewartson system in three dimension. Communications on Pure & Applied Analysis, 2015, 14 (5) : 16411670. doi: 10.3934/cpaa.2015.14.1641 
[4] 
Zaihui Gan, Boling Guo, Jian Zhang. Sharp threshold of global existence for the generalized DaveyStewartson system in $R^2$. Communications on Pure & Applied Analysis, 2009, 8 (3) : 913922. doi: 10.3934/cpaa.2009.8.913 
[5] 
J. Colliander, Justin Holmer, Monica Visan, Xiaoyi Zhang. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure & Applied Analysis, 2008, 7 (3) : 467489. doi: 10.3934/cpaa.2008.7.467 
[6] 
Olivier Goubet, Manal Hussein. Global attractor for the DaveyStewartson system on $\mathbb R^2$. Communications on Pure & Applied Analysis, 2009, 8 (5) : 15551575. doi: 10.3934/cpaa.2009.8.1555 
[7] 
Satoshi Masaki. A sharp scattering condition for focusing masssubcritical nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2015, 14 (4) : 14811531. doi: 10.3934/cpaa.2015.14.1481 
[8] 
Chenmin Sun, Hua Wang, Xiaohua Yao, Jiqiang Zheng. Scattering below ground state of focusing fractional nonlinear Schrödinger equation with radial data. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 22072228. doi: 10.3934/dcds.2018091 
[9] 
Caroline Obrecht, J.C. Saut. Remarks on the full dispersion DaveyStewartson systems. Communications on Pure & Applied Analysis, 2015, 14 (4) : 15471561. doi: 10.3934/cpaa.2015.14.1547 
[10] 
Xing Cheng, Ze Li, Lifeng Zhao. Scattering of solutions to the nonlinear Schrödinger equations with regular potentials. Discrete & Continuous Dynamical Systems  A, 2017, 37 (6) : 29993023. doi: 10.3934/dcds.2017129 
[11] 
Van Duong Dinh. On blowup solutions to the focusing masscritical nonlinear fractional Schrödinger equation. Communications on Pure & Applied Analysis, 2019, 18 (2) : 689708. doi: 10.3934/cpaa.2019034 
[12] 
Younghun Hong. Scattering for a nonlinear Schrödinger equation with a potential. Communications on Pure & Applied Analysis, 2016, 15 (5) : 15711601. doi: 10.3934/cpaa.2016003 
[13] 
Christian Klein, Benson Muite, Kristelle Roidot. Numerical study of blowup in the DaveyStewartson system. Discrete & Continuous Dynamical Systems  B, 2013, 18 (5) : 13611387. doi: 10.3934/dcdsb.2013.18.1361 
[14] 
Rémi Carles. Global existence results for nonlinear Schrödinger equations with quadratic potentials. Discrete & Continuous Dynamical Systems  A, 2005, 13 (2) : 385398. doi: 10.3934/dcds.2005.13.385 
[15] 
Zaihui Gan, Boling Guo, Jian Zhang. Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials. Communications on Pure & Applied Analysis, 2009, 8 (4) : 13031312. doi: 10.3934/cpaa.2009.8.1303 
[16] 
Masahoto Ohta, Grozdena Todorova. Remarks on global existence and blowup for damped nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems  A, 2009, 23 (4) : 13131325. doi: 10.3934/dcds.2009.23.1313 
[17] 
Daiwen Huang, Jingjun Zhang. Global smooth solutions for the nonlinear Schrödinger equation with magnetic effect. Discrete & Continuous Dynamical Systems  S, 2016, 9 (6) : 17531773. doi: 10.3934/dcdss.2016073 
[18] 
Takahisa Inui. Global dynamics of solutions with group invariance for the nonlinear schrödinger equation. Communications on Pure & Applied Analysis, 2017, 16 (2) : 557590. doi: 10.3934/cpaa.2017028 
[19] 
TaiChia Lin, TsungFang Wu. Existence and multiplicity of positive solutions for two coupled nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems  A, 2013, 33 (7) : 29112938. doi: 10.3934/dcds.2013.33.2911 
[20] 
D.G. deFigueiredo, Yanheng Ding. Solutions of a nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  A, 2002, 8 (3) : 563584. doi: 10.3934/dcds.2002.8.563 
2018 Impact Factor: 0.925
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