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On the hyperbolicity of homoclinic classes
KdV cnoidal waves are spectrally stable
1. | Department of Applied Mathematics, University of Washington, Campus box 352420, Seattle, WA 98195, United States |
2. | Department of Applied Mathematics, University of Washington, Campus Box 352420, Seattle, WA 98195, United States |
[1] |
S. Raynor, G. Staffilani. Low regularity stability of solitons for the KDV equation. Communications on Pure and Applied Analysis, 2003, 2 (3) : 277-296. doi: 10.3934/cpaa.2003.2.277 |
[2] |
Yuqian Zhou, Qian Liu. Reduction and bifurcation of traveling waves of the KdV-Burgers-Kuramoto equation. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 2057-2071. doi: 10.3934/dcdsb.2016036 |
[3] |
Jundong Wang, Lijun Zhang, Elena Shchepakina, Vladimir Sobolev. Solitary waves of singularly perturbed generalized KdV equation with high order nonlinearity. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022124 |
[4] |
H. Kalisch. Stability of solitary waves for a nonlinearly dispersive equation. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 709-717. doi: 10.3934/dcds.2004.10.709 |
[5] |
Michael Herrmann, Alice Mikikits-Leitner. KdV waves in atomic chains with nonlocal interactions. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2047-2067. doi: 10.3934/dcds.2016.36.2047 |
[6] |
Juan-Ming Yuan, Jiahong Wu. The complex KdV equation with or without dissipation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 489-512. doi: 10.3934/dcdsb.2005.5.489 |
[7] |
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 |
[8] |
Steve Levandosky, Yue Liu. Stability and weak rotation limit of solitary waves of the Ostrovsky equation. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 793-806. doi: 10.3934/dcdsb.2007.7.793 |
[9] |
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 |
[10] |
François Genoud. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1229-1247. doi: 10.3934/dcds.2009.25.1229 |
[11] |
Khaled El Dika. Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 583-622. doi: 10.3934/dcds.2005.13.583 |
[12] |
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 |
[13] |
Annie Millet, Svetlana Roudenko. Generalized KdV equation subject to a stochastic perturbation. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1177-1198. doi: 10.3934/dcdsb.2018147 |
[14] |
Rowan Killip, Soonsik Kwon, Shuanglin Shao, Monica Visan. On the mass-critical generalized KdV equation. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 191-221. doi: 10.3934/dcds.2012.32.191 |
[15] |
María Santos Bruzón, Tamara María Garrido. Symmetries and conservation laws of a KdV6 equation. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 631-641. doi: 10.3934/dcdss.2018038 |
[16] |
Xingxing Liu. Stability in the energy space of the sum of $ N $ solitary waves for an equation modelling shallow water waves of moderate amplitude. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022105 |
[17] |
Brian Pigott, Sarah Raynor. Long-term stability for kdv solitons in weighted Hs spaces. Communications on Pure and Applied Analysis, 2017, 16 (2) : 393-416. doi: 10.3934/cpaa.2017020 |
[18] |
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 |
[19] |
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 |
[20] |
Luyi Ma, Hong-Tao Niu, Zhi-Cheng Wang. Global asymptotic stability of traveling waves to the Allen-Cahn equation with a fractional Laplacian. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2457-2472. doi: 10.3934/cpaa.2019111 |
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