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Remarks on the orbital instability of standing waves for the wave-Schrödinger system in higher dimensions
| 1. | Department of Mathematics, Hokkaido University Kita 10, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan |
| [1] |
Takafumi Akahori. Global solutions of the wave-Schrödinger system with rough data. Communications on Pure & Applied Analysis, 2005, 4 (2) : 209-240. doi: 10.3934/cpaa.2005.4.209 |
| [2] |
Masahito Ohta. Strong instability of standing waves for nonlinear Schrödinger equations with a partial confinement. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1671-1680. doi: 10.3934/cpaa.2018080 |
| [3] |
Reika Fukuizumi. Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. Discrete & Continuous Dynamical Systems - A, 2001, 7 (3) : 525-544. doi: 10.3934/dcds.2001.7.525 |
| [4] |
Jun-ichi 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) : 843-859. doi: 10.3934/cpaa.2015.14.843 |
| [5] |
Fábio Natali, Ademir Pastor. Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 221-238. doi: 10.3934/dcds.2011.31.221 |
| [6] |
Zhi Chen, Xianhua Tang, Ning Zhang, Jian Zhang. Standing waves for Schrödinger-Poisson system with general nonlinearity. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 6103-6129. doi: 10.3934/dcds.2019266 |
| [7] |
Ademir Pastor. On three-wave interaction Schrödinger systems with quadratic nonlinearities: Global well-posedness and standing waves. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2217-2242. doi: 10.3934/cpaa.2019100 |
| [8] |
Fábio Natali, Ademir Pastor. Stability properties of periodic standing waves for the Klein-Gordon-Schrödinger system. Communications on Pure & Applied Analysis, 2010, 9 (2) : 413-430. doi: 10.3934/cpaa.2010.9.413 |
| [9] |
Akihiro Shimomura. Modified wave operators for the coupled wave-Schrödinger equations in three space dimensions. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1571-1586. doi: 10.3934/dcds.2003.9.1571 |
| [10] |
Sevdzhan Hakkaev. Orbital stability of solitary waves of the Schrödinger-Boussinesq equation. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1043-1050. doi: 10.3934/cpaa.2007.6.1043 |
| [11] |
Yohei Yamazaki. Transverse instability for a system of nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 565-588. doi: 10.3934/dcdsb.2014.19.565 |
| [12] |
Huifang Jia, Gongbao Li, Xiao Luo. Stable standing waves for cubic nonlinear Schrödinger systems with partial confinement. Discrete & Continuous Dynamical Systems - A, 2020, 40 (5) : 2739-2766. doi: 10.3934/dcds.2020148 |
| [13] |
Xiaoyu Zeng. Asymptotic properties of standing waves for mass subcritical nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1749-1762. doi: 10.3934/dcds.2017073 |
| [14] |
Yue Liu. Existence of unstable standing waves for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2008, 7 (1) : 193-209. doi: 10.3934/cpaa.2008.7.193 |
| [15] |
François Genoud, Charles A. Stuart. Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 137-186. doi: 10.3934/dcds.2008.21.137 |
| [16] |
François Genoud. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1229-1247. doi: 10.3934/dcds.2009.25.1229 |
| [17] |
Soohyun Bae, Jaeyoung Byeon. Standing waves of nonlinear Schrödinger equations with optimal conditions for potential and nonlinearity. Communications on Pure & Applied Analysis, 2013, 12 (2) : 831-850. doi: 10.3934/cpaa.2013.12.831 |
| [18] |
Jaeyoung Byeon, Ohsang Kwon, Yoshihito Oshita. Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations. Communications on Pure & Applied Analysis, 2015, 14 (3) : 825-842. doi: 10.3934/cpaa.2015.14.825 |
| [19] |
José R. Quintero, Juan C. Cordero. Instability of the standing waves for a Benney-Roskes/Zakharov-Rubenchik system and blow-up for the Zakharov equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1213-1240. doi: 10.3934/dcdsb.2019217 |
| [20] |
Alex H. Ardila. Stability of standing waves for a nonlinear SchrÖdinger equation under an external magnetic field. Communications on Pure & Applied Analysis, 2018, 17 (1) : 163-175. doi: 10.3934/cpaa.2018010 |
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