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Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation
1. | IACS-FSB, Section de Mathématiques, École Polytechnique Fédérale de Lausanne CH-1015 Lausanne, Switzerland |
[1] |
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 and Applied Analysis, 2015, 14 (3) : 843-859. doi: 10.3934/cpaa.2015.14.843 |
[2] |
Hiroaki Kikuchi. Remarks on the orbital instability of standing waves for the wave-Schrödinger system in higher dimensions. Communications on Pure and Applied Analysis, 2010, 9 (2) : 351-364. doi: 10.3934/cpaa.2010.9.351 |
[3] |
Fábio Natali, Ademir Pastor. Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 221-238. doi: 10.3934/dcds.2011.31.221 |
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Sevdzhan Hakkaev. Orbital stability of solitary waves of the Schrödinger-Boussinesq equation. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1043-1050. doi: 10.3934/cpaa.2007.6.1043 |
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Aslihan Demirkaya, Panayotis G. Kevrekidis, Milena Stanislavova, Atanas Stefanov. Spectral stability analysis for standing waves of a perturbed Klein-Gordon equation. Conference Publications, 2015, 2015 (special) : 359-368. doi: 10.3934/proc.2015.0359 |
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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) : 137-186. doi: 10.3934/dcds.2008.21.137 |
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Marco Ghimenti, Stefan Le Coz, Marco Squassina. On the stability of standing waves of Klein-Gordon equations in a semiclassical regime. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2389-2401. 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) : 525-544. doi: 10.3934/dcds.2001.7.525 |
[9] |
Salvador Cruz-García, Catherine García-Reimbert. On the spectral stability of standing waves of the one-dimensional $M^5$-model. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1079-1099. 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) : 2187-2209. doi: 10.3934/cpaa.2021063 |
[11] |
Giovana Alves, Fábio Natali. Periodic waves for the cubic-quintic nonlinear Schrodinger equation: Existence and orbital stability. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022101 |
[12] |
Fábio Natali, Ademir Pastor. Stability properties of periodic standing waves for the Klein-Gordon-Schrödinger system. Communications on Pure and Applied Analysis, 2010, 9 (2) : 413-430. doi: 10.3934/cpaa.2010.9.413 |
[13] |
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) : 163-175. doi: 10.3934/cpaa.2018010 |
[14] |
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) : 121-136. doi: 10.3934/dcds.2008.21.121 |
[15] |
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) : 5837-5879. doi: 10.3934/dcds.2016057 |
[16] |
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) : 197-209. doi: 10.3934/dcdsb.2018097 |
[17] |
Yue Zhang, Jian Zhang. Stability and instability of standing waves for Gross-Pitaevskii equations with double power nonlinearities. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022007 |
[18] |
Michael Herrmann. Homoclinic standing waves in focusing DNLS equations. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 737-752. doi: 10.3934/dcds.2011.31.737 |
[19] |
Michiel Bertsch, Hirofumi Izuhara, Masayasu Mimura, Tohru Wakasa. Standing and travelling waves in a parabolic-hyperbolic system. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5603-5635. doi: 10.3934/dcds.2019246 |
[20] |
José Manuel Palacios. Orbital and asymptotic stability of a train of peakons for the Novikov equation. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2475-2518. doi: 10.3934/dcds.2020372 |
2021 Impact Factor: 1.588
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