
Previous Article
Quasiinvariant measures, escape rates and the effect of the hole
 DCDS Home
 This Issue

Next Article
Non topologically weakly mixing interval exchanges
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] 
Boling Guo, Jun Wu. Wellposedness of the initialboundary value problem for the fourthorder nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021205 
[4] 
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 
[5] 
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 
[6] 
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 
[7] 
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 
[8] 
Lassaad Aloui, Slim Tayachi. Local wellposedness for the inhomogeneous nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems, 2021, 41 (11) : 54095437. doi: 10.3934/dcds.2021082 
[9] 
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 
[10] 
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 
[11] 
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 
[12] 
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 
[13] 
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 
[14] 
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 
[15] 
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 
[16] 
Massimo Cicognani, Michael Reissig. Wellposedness for degenerate Schrödinger equations. Evolution Equations & Control Theory, 2014, 3 (1) : 1533. doi: 10.3934/eect.2014.3.15 
[17] 
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 
[18] 
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 
[19] 
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 
[20] 
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 
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]