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Long time dynamics near the symmetry breaking bifurcation for nonlinear Schrödinger/GrossPitaevskii equations
1.  Department of Applied Physics and Applied Mathematics, Columbia University, 200 S. W. Mudd, 500 W. 120th St., New York City, NY 10027, United States, United States 
[1] 
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 
[2] 
Thomas Bartsch, Zhongwei Tang. Multibump solutions of nonlinear Schrödinger equations with steep potential well and indefinite potential. Discrete & Continuous Dynamical Systems  A, 2013, 33 (1) : 726. doi: 10.3934/dcds.2013.33.7 
[3] 
Wulong Liu, Guowei Dai. Multiple solutions for a fractional nonlinear Schrödinger equation with local potential. Communications on Pure & Applied Analysis, 2017, 16 (6) : 21052123. doi: 10.3934/cpaa.2017104 
[4] 
Reika Fukuizumi. Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. Discrete & Continuous Dynamical Systems  A, 2001, 7 (3) : 525544. doi: 10.3934/dcds.2001.7.525 
[5] 
Naoufel Ben Abdallah, Yongyong Cai, Francois Castella, Florian Méhats. Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential. Kinetic & Related Models, 2011, 4 (4) : 831856. doi: 10.3934/krm.2011.4.831 
[6] 
César E. Torres Ledesma. Existence and concentration of solutions for a nonlinear fractional Schrödinger equation with steep potential well. Communications on Pure & Applied Analysis, 2016, 15 (2) : 535547. doi: 10.3934/cpaa.2016.15.535 
[7] 
Grégoire Allaire, M. Vanninathan. Homogenization of the Schrödinger equation with a time oscillating potential. Discrete & Continuous Dynamical Systems  B, 2006, 6 (1) : 116. doi: 10.3934/dcdsb.2006.6.1 
[8] 
Jian Zhang, Shihui Zhu, Xiaoguang Li. Rate of $L^2$concentration of the blowup solution for critical nonlinear Schrödinger equation with potential. Mathematical Control & Related Fields, 2011, 1 (1) : 119127. doi: 10.3934/mcrf.2011.1.119 
[9] 
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 
[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  A, 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  A, 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] 
Junichi Segata. Wellposedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation. Discrete & Continuous Dynamical Systems  A, 2010, 27 (3) : 10931105. doi: 10.3934/dcds.2010.27.1093 
[15] 
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 
[16] 
Benjamin Dodson. Global wellposedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linearnonlinear decomposition. Discrete & Continuous Dynamical Systems  A, 2013, 33 (5) : 19051926. doi: 10.3934/dcds.2013.33.1905 
[17] 
Liping Wang, Chunyi Zhao. Infinitely many solutions for nonlinear Schrödinger equations with slow decaying of potential. Discrete & Continuous Dynamical Systems  A, 2017, 37 (3) : 17071731. doi: 10.3934/dcds.2017071 
[18] 
Guanghua Shi, Dongfeng Yan. KAM tori for quintic nonlinear schrödinger equations with given potential. Discrete & Continuous Dynamical Systems  A, 2020, 40 (4) : 24212439. doi: 10.3934/dcds.2020120 
[19] 
Myeongju Chae, Soonsik Kwon. The stability of nonlinear Schrödinger equations with a potential in high Sobolev norms revisited. Communications on Pure & Applied Analysis, 2016, 15 (2) : 341365. doi: 10.3934/cpaa.2016.15.341 
[20] 
Zuji Guo. Nodal solutions for nonlinear Schrödinger equations with decaying potential. Communications on Pure & Applied Analysis, 2016, 15 (4) : 11251138. doi: 10.3934/cpaa.2016.15.1125 
2019 Impact Factor: 1.338
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