A property of exponential stability in nonlinear wave equations near the fundamental linear mode
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Publication:1808325
DOI10.1016/S0167-2789(98)00169-9zbMath0937.35010OpenAlexW1976173011MaRDI QIDQ1808325
Dario Bambusi, Nikolaiĭ N. Nekhoroshev
Publication date: 6 December 1999
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0167-2789(98)00169-9
Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35) Second-order nonlinear hyperbolic equations (35L70) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)
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Cites Work
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- Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
- Semigroups of linear operators and applications to partial differential equations
- The separation of motions in systems with rapidly rotating phase
- Stability of motions near resonances in quasi-integrable Hamiltonian systems
- Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. I
- Fine tuning of resonances and periodic solutions of Hamiltonian systems near equilibrium
- Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
- Manifolds, tensor analysis, and applications.
- Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
- Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems
- Nekhoroshev estimates for quasi-convex Hamiltonian systems
- Periodic solutions of the equation \(u_{tt}-u_{xx}+u^ 3=0\)
- A Nekhoroshev-type theorem for Hamiltonian systems with infinitely many degrees of freedom
- Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. II
- On the periodic motions near a given periodic motion of a dynamical system
- The nonlinear Klein-Gordon equation on an interval as a perturbed sine-Gordon equation
- Construction of periodic solutions of nonlinear wave equations in higher dimension
- Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
- Periodic solutions of a class of hyperbolic equations containing a small parameter
- Behavior of Hamiltonian systems close to integrable
- Periodic solutions of nonlinear vibrating strings and duality principles
- A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
- PERTURBATION OF QUASIPERIODIC SOLUTIONS OF INFINITE-DIMENSIONAL HAMILTONIAN SYSTEMS
- Periodic solutions of hamiltonian systems
- AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
- Complex analysis and convolution operators
- Newton's method and periodic solutions of nonlinear wave equations
- Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators
- Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations
- Regularization of kepler's problem and the averaging method on a manifold
- Riemannian geometry