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Wellposedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation
1.  Department of Mathematics, Fukuoka University of Education, 11 Bunkyoumachi Akama, Munakata City, Fukuoka, 8114192, Japan 
[1] 
Hiroyuki Hirayama, Mamoru Okamoto. Wellposedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity. Communications on Pure & Applied Analysis, 2016, 15 (3) : 831851. doi: 10.3934/cpaa.2016.15.831 
[2] 
Yuanyuan Ren, Yongsheng Li, Wei Yan. Sharp wellposedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2018, 17 (2) : 487504. doi: 10.3934/cpaa.2018027 
[3] 
Junichi Segata. Initial value problem for the fourth order nonlinear Schrödinger type equation on torus and orbital stability of standing waves. Communications on Pure & Applied Analysis, 2015, 14 (3) : 843859. doi: 10.3934/cpaa.2015.14.843 
[4] 
Xuan Liu, Ting Zhang. Local wellposedness and finite time blowup for fourthorder Schrödinger equation with complex coefficient. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021156 
[5] 
Tarek Saanouni. Global wellposedness of some highorder semilinear wave and Schrödinger type equations with exponential nonlinearity. Communications on Pure & Applied Analysis, 2014, 13 (1) : 273291. doi: 10.3934/cpaa.2014.13.273 
[6] 
Ademir Pastor. On threewave interaction Schrödinger systems with quadratic nonlinearities: Global wellposedness and standing waves. Communications on Pure & Applied Analysis, 2019, 18 (5) : 22172242. doi: 10.3934/cpaa.2019100 
[7] 
Lassaad Aloui, Slim Tayachi. Local wellposedness for the inhomogeneous nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021082 
[8] 
Changxing Miao, Bo Zhang. Global wellposedness of the Cauchy problem for nonlinear Schrödingertype equations. Discrete & Continuous Dynamical Systems, 2007, 17 (1) : 181200. doi: 10.3934/dcds.2007.17.181 
[9] 
Takafumi Akahori. Low regularity global wellposedness for the nonlinear Schrödinger equation on closed manifolds. Communications on Pure & Applied Analysis, 2010, 9 (2) : 261280. doi: 10.3934/cpaa.2010.9.261 
[10] 
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global wellposedness for a periodic nonlinear Schrödinger equation in 1D and 2D. Discrete & Continuous Dynamical Systems, 2007, 19 (1) : 3765. doi: 10.3934/dcds.2007.19.37 
[11] 
Zihua Guo, Yifei Wu. Global wellposedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 257264. doi: 10.3934/dcds.2017010 
[12] 
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global wellposedness for the $L^2$ critical nonlinear Schrödinger equation in higher dimensions. Communications on Pure & Applied Analysis, 2007, 6 (4) : 10231041. doi: 10.3934/cpaa.2007.6.1023 
[13] 
Zhong Wang. Stability of Hasimoto solitons in energy space for a fourth order nonlinear Schrödinger type equation. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 40914108. doi: 10.3934/dcds.2017174 
[14] 
Benjamin Dodson. Global wellposedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linearnonlinear decomposition. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 19051926. doi: 10.3934/dcds.2013.33.1905 
[15] 
Massimo Cicognani, Michael Reissig. Wellposedness for degenerate Schrödinger equations. Evolution Equations & Control Theory, 2014, 3 (1) : 1533. doi: 10.3934/eect.2014.3.15 
[16] 
Huafei Di, Yadong Shang, Xiaoxiao Zheng. Global wellposedness for a fourth order pseudoparabolic equation with memory and source terms. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 781801. doi: 10.3934/dcdsb.2016.21.781 
[17] 
Shaoming Guo, Xianfeng Ren, Baoxiang Wang. Local wellposedness for the derivative nonlinear Schrödinger equation with $ L^2 $subcritical data. Discrete & Continuous Dynamical Systems, 2021, 41 (9) : 42074253. doi: 10.3934/dcds.2021034 
[18] 
Jibin Li, Yan Zhou. Bifurcations and exact traveling wave solutions for the nonlinear Schrödinger equation with fourthorder dispersion and dual power law nonlinearity. Discrete & Continuous Dynamical Systems  S, 2020, 13 (11) : 30833097. doi: 10.3934/dcdss.2020113 
[19] 
Takeshi Wada. A remark on local wellposedness for nonlinear Schrödinger equations with power nonlinearityan alternative approach. Communications on Pure & Applied Analysis, 2019, 18 (3) : 13591374. doi: 10.3934/cpaa.2019066 
[20] 
Hiroyuki Hirayama. Wellposedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data. Communications on Pure & Applied Analysis, 2014, 13 (4) : 15631591. doi: 10.3934/cpaa.2014.13.1563 
2019 Impact Factor: 1.338
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