相关论文: On the existence of quasi-periodic lattice oscilla…

We consider one dimensional chains of interacting particles subjected to one dimensional almost-periodic media. We formulate and prove two KAM type theorems corresponding to both short-range and long-range interactions respectively. Both…

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 consider nonlinear Schrodinger systems with periodic boundary condition in high dimension. We establish an abstract infinite dimensional KAM theorem and apply it to the nonlinear Schrodinger equation systems with real…

We consider the one dimensional space-periodic Vlasov-Poisson equations and construct, close to symmetric flat velocity strips, small amplitude traveling quasi-periodic electron-layers, namely strip-shaped patches of electrons in the phase…

We study waves in a chain of dispersively coupled phase oscillators. Two approaches -- a quasi-continuous approximation and an iterative numerical solution of the lattice equation -- allow us to characterize different types of traveling…

In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal…

In this paper, we shall implement KAM theory in order to construct a large class of time quasi-periodic solutions for an active scalar model arising in fluid dynamics. More precisely, the construction of invariant tori is performed for…

Written with respect to an appropriate Poisson structure, a partially integrable Hamiltonian system is viewed as a completely integrable system with parameters. Then, the theorem on quasi-periodic stability in Ref. [1] (the KAM theorem) can…

We establish the existence of quasi-periodic traveling wave solutions for the $\beta$-plane equation on $\mathbb{T}^2$ with a large quasi-periodic traveling wave external force. These solutions exhibit large sizes, which depend on the…

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 dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…

We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…

We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the…

We employ the Craig-Wayne-Bourgain method to construct quasi-periodic solutions for delayed perturbation differential equations. Our results not only implement the existing literatures on constructing quasi-periodic solutions for DDE by the…

Quasi-periodic solutions with Liouvillean frequency of forced nonlinear Schr\"odinger equation are constructed. This is based on an infinite dimensional KAM theory for Liouvillean frequency.

It has been recently argued that near-integrable nonautonomous one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even when the time-dependent (nonintegrable) part of the Hamiltonian is given in the form of a…

Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…

We present the recent result [8] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the first existence result of quasi-periodic water waves solutions…

In the present paper we study phase waves of self-sustained oscillators with a nearest neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics we approximate the lattice with a quasi-continuum, QC. The…

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…