相关论文: KAM theory for the Hamiltonian derivative wave equ…

We prove the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. This result is…

In this note we present a new KAM result which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is…

The existence of lower dimensional KAM tori is shown for a class of nearly integrable Hamiltonian systems where the second Melnikov's conditions are eliminated. As a consequence, it is proved that there exist many invariant tori and thus…

Given $l>2\nu>2d\geq 4$, we prove the persistence of a Cantor--family of KAM tori of measure $O(\varepsilon^{1/2-\nu/l})$ for any non--degenerate nearly integrable Hamiltonian system of class $C^l(\mathscr D\times\mathbb{T}^d)$, where…

In this paper, we investigate the existence of KAM tori for an infinite dimensional Hamiltonian system with finite number of zero normal frequencies. By constructing a constant quantity we show that, for "most" frequencies in the sense of…

We suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the…

Introduce several KAM theorems for infinite dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori. Especially, introduce a KAM theorem in the paper(Cummun. Math.…

We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamiltonian differentiable perturbations of the mKdV equation. The proof is…

We prove the existence and stability of Cantor families of quasi-periodic, small amplitude solutions of quasi-linear (i.e. strongly nonlinear) autonomous Hamiltonian perturbations of KdV.

In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians systems. This result extends previous works of S.B. Kuksin and J. P\"oschel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an application we…

In this paper, we establish an abstract infinite dimensional KAM theorem dealing with normal frequencies in weaker spectral asymptotics \Omega_{i}(\xi)=i^d+o(i^{d})+o(i^{\delta}), where $d>0, \delta<0$, which can be applied to a large class…

We proved a KAM theorem on existence of invariant tori in generalized Hamiltonian systems without action-angle variables. It is a generalization of the result of de la Llave et al. [Llave, 2005] that deals with canonical Hamiltonian system.

We provide a symplectic reduction of a partially integrable Hamiltonian system to a completely integrable one. The KAM theorem is applied to this reduced completely integrable Hamiltonian system. Its KAM perturbation generates a…

In this paper, one-dimensional (1D) nonlinear wave equations $u_{tt} -u_{xx}+V(x)u =f(u)$, with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function…

We prove an infinite-dimensional KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. As an application, we prove the reducibility of the linear fractional Schr\"odinger equation with quasi-periodic…

In the paper, we prove an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems. Using this KAM theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of reversible…

We consider Gevrey perturbations $H$ of a completely integrable Gevrey Hamiltonian $H_0$. Given a Cantor set $\Omega_\kappa$ defined by a Diophantine condition, we find a family of KAM invariant tori of $H$ with frequencies $\omega\in…

It is proved that the KAM tori (thus quasi-periodic solutions) are long time stable for infinite dimensional Hamiltonian systems generated by nonlinear wave equation, by constructing a partial normal form of higher order around the KAM…

We develop an abstract KAM theorem for systems of infinitely many interacting particles with decaying masses and all-to-all interactions. Using this framework, we construct full-dimensional KAM tori for infinite-dimensional mechanical…

In this paper, we present two infinite-dimensional KAM theorems with frequency-preserving for a nonresonant frequency of Diophantine type or even weaker. To be more precise, under a nondegenerate condition for an infinite-dimensional…