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Quasi-periodic solutions of nonlinear wave equations with a prescribed potential
On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition
1. | Department of Mathematics, Southeast University, Nanjing 210096, China |
2. | Department of Mathematics, Southeast University, Nanjing 211189, China |
[1] |
Xiaocai Wang, Junxiang Xu. Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 701-718. doi: 10.3934/dcds.2009.25.701 |
[2] |
Wen Si, Fenfen Wang, Jianguo Si. Almost-periodic perturbations of non-hyperbolic equilibrium points via Pöschel-Rüssmann KAM method. Communications on Pure and Applied Analysis, 2020, 19 (1) : 541-585. doi: 10.3934/cpaa.2020027 |
[3] |
Claire Chavaudret, Stefano Marmi. Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition. Journal of Modern Dynamics, 2012, 6 (1) : 59-78. doi: 10.3934/jmd.2012.6.59 |
[4] |
Helmut Rüssmann. KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character. Discrete and Continuous Dynamical Systems - S, 2010, 3 (4) : 683-718. doi: 10.3934/dcdss.2010.3.683 |
[5] |
Fuzhong Cong, Yong Li. Invariant hyperbolic tori for Hamiltonian systems with degeneracy. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 371-382. doi: 10.3934/dcds.1997.3.371 |
[6] |
Pedro J. Torres, Zhibo Cheng, Jingli Ren. Non-degeneracy and uniqueness of periodic solutions for $2n$-order differential equations. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2155-2168. doi: 10.3934/dcds.2013.33.2155 |
[7] |
Lipeng Duan, Jun Yang. On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4767-4790. doi: 10.3934/dcds.2021056 |
[8] |
Robert Magnus, Olivier Moschetta. The non-linear Schrödinger equation with non-periodic potential: infinite-bump solutions and non-degeneracy. Communications on Pure and Applied Analysis, 2012, 11 (2) : 587-626. doi: 10.3934/cpaa.2012.11.587 |
[9] |
Genni Fragnelli, Dimitri Mugnai. Singular parabolic equations with interior degeneracy and non smooth coefficients: The Neumann case. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1495-1511. doi: 10.3934/dcdss.2020084 |
[10] |
Claire Chavaudret, Stefano Marmi. Erratum: Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition. Journal of Modern Dynamics, 2015, 9: 285-287. doi: 10.3934/jmd.2015.9.285 |
[11] |
Peter Giesl. Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 355-373. doi: 10.3934/dcds.2007.18.355 |
[12] |
Nadia Lekrine, Chao-Jiang Xu. Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation. Kinetic and Related Models, 2009, 2 (4) : 647-666. doi: 10.3934/krm.2009.2.647 |
[13] |
Alicia Cordero, José Martínez Alfaro, Pura Vindel. Bott integrable Hamiltonian systems on $S^{2}\times S^{1}$. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 587-604. doi: 10.3934/dcds.2008.22.587 |
[14] |
Peter Šepitka. Riccati equations for linear Hamiltonian systems without controllability condition. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1685-1730. doi: 10.3934/dcds.2019074 |
[15] |
Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 |
[16] |
Xuemei Li, Zaijiu Shang. On the existence of invariant tori in non-conservative dynamical systems with degeneracy and finite differentiability. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 4225-4257. doi: 10.3934/dcds.2019171 |
[17] |
Sandra Lucente, Eugenio Montefusco. Non-hamiltonian Schrödinger systems. Discrete and Continuous Dynamical Systems - S, 2013, 6 (3) : 761-770. doi: 10.3934/dcdss.2013.6.761 |
[18] |
Pedro Roberto de Lima, Hugo D. Fernández Sare. General condition for exponential stability of thermoelastic Bresse systems with Cattaneo's law. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3575-3596. doi: 10.3934/cpaa.2020156 |
[19] |
Sonja Hohloch, Silvia Sabatini, Daniele Sepe. From compact semi-toric systems to Hamiltonian $S^1$-spaces. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 247-281. doi: 10.3934/dcds.2015.35.247 |
[20] |
Plamen Stefanov, Yang Yang. Multiwave tomography with reflectors: Landweber's iteration. Inverse Problems and Imaging, 2017, 11 (2) : 373-401. doi: 10.3934/ipi.2017018 |
2020 Impact Factor: 1.392
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