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Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation
1.  IACSFSB, Section de Mathématiques, École Polytechnique Fédérale de Lausanne CH1015 Lausanne, Switzerland 
[1] 
Junichi Segata. Initial value problem for the fourth order nonlinear Schrödinger type equation on torus and orbital stability of standing waves. Communications on Pure and Applied Analysis, 2015, 14 (3) : 843859. doi: 10.3934/cpaa.2015.14.843 
[2] 
Hiroaki Kikuchi. Remarks on the orbital instability of standing waves for the waveSchrödinger system in higher dimensions. Communications on Pure and Applied Analysis, 2010, 9 (2) : 351364. doi: 10.3934/cpaa.2010.9.351 
[3] 
Fábio Natali, Ademir Pastor. Orbital stability of periodic waves for the KleinGordonSchrödinger system. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 221238. doi: 10.3934/dcds.2011.31.221 
[4] 
Sevdzhan Hakkaev. Orbital stability of solitary waves of the SchrödingerBoussinesq equation. Communications on Pure and Applied Analysis, 2007, 6 (4) : 10431050. doi: 10.3934/cpaa.2007.6.1043 
[5] 
Aslihan Demirkaya, Panayotis G. Kevrekidis, Milena Stanislavova, Atanas Stefanov. Spectral stability analysis for standing waves of a perturbed KleinGordon equation. Conference Publications, 2015, 2015 (special) : 359368. doi: 10.3934/proc.2015.0359 
[6] 
François Genoud, Charles A. Stuart. Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 137186. doi: 10.3934/dcds.2008.21.137 
[7] 
Marco Ghimenti, Stefan Le Coz, Marco Squassina. On the stability of standing waves of KleinGordon equations in a semiclassical regime. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 23892401. doi: 10.3934/dcds.2013.33.2389 
[8] 
Reika Fukuizumi. Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 525544. doi: 10.3934/dcds.2001.7.525 
[9] 
Salvador CruzGarcía, Catherine GarcíaReimbert. On the spectral stability of standing waves of the onedimensional $M^5$model. Discrete and Continuous Dynamical Systems  B, 2016, 21 (4) : 10791099. doi: 10.3934/dcdsb.2016.21.1079 
[10] 
Andrew Comech, Elena Kopylova. Orbital stability and spectral properties of solitary waves of Klein–Gordon equation with concentrated nonlinearity. Communications on Pure and Applied Analysis, 2021, 20 (6) : 21872209. doi: 10.3934/cpaa.2021063 
[11] 
Fábio Natali, Ademir Pastor. Stability properties of periodic standing waves for the KleinGordonSchrödinger system. Communications on Pure and Applied Analysis, 2010, 9 (2) : 413430. doi: 10.3934/cpaa.2010.9.413 
[12] 
Alex H. Ardila. Stability of standing waves for a nonlinear SchrÖdinger equation under an external magnetic field. Communications on Pure and Applied Analysis, 2018, 17 (1) : 163175. doi: 10.3934/cpaa.2018010 
[13] 
Reika Fukuizumi, Louis Jeanjean. Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 121136. doi: 10.3934/dcds.2008.21.121 
[14] 
Riccardo Adami, Diego Noja, Cecilia Ortoleva. Asymptotic stability for standing waves of a NLS equation with subcritical concentrated nonlinearity in dimension three: Neutral modes. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 58375879. doi: 10.3934/dcds.2016057 
[15] 
Aslihan Demirkaya, Milena Stanislavova. Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation. Discrete and Continuous Dynamical Systems  B, 2019, 24 (1) : 197209. doi: 10.3934/dcdsb.2018097 
[16] 
Yue Zhang, Jian Zhang. Stability and instability of standing waves for GrossPitaevskii equations with double power nonlinearities. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022007 
[17] 
Michael Herrmann. Homoclinic standing waves in focusing DNLS equations. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 737752. doi: 10.3934/dcds.2011.31.737 
[18] 
Michiel Bertsch, Hirofumi Izuhara, Masayasu Mimura, Tohru Wakasa. Standing and travelling waves in a parabolichyperbolic system. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 56035635. doi: 10.3934/dcds.2019246 
[19] 
José Manuel Palacios. Orbital and asymptotic stability of a train of peakons for the Novikov equation. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 24752518. doi: 10.3934/dcds.2020372 
[20] 
Yonggeun Cho, Hichem Hajaiej, Gyeongha Hwang, Tohru Ozawa. On the orbital stability of fractional Schrödinger equations. Communications on Pure and Applied Analysis, 2014, 13 (3) : 12671282. doi: 10.3934/cpaa.2014.13.1267 
2020 Impact Factor: 1.392
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