有阻尼和外力驱动的离散非线性Schrdinger方程离散呼吸子的存在性和稳定性

Existence and stability of discrete breathers of driven and damped discrete nonlinear Schrdinger equation

主要研究一维格点系统中有阻尼和Ac-驱动的DNLS方程的离散呼吸子的存在性和稳定性.通常所用的同宿轨的方法只能给出数值模拟,而不能得到严格的证明.因此我们先考虑其单个振子的周期解,然后给出在R×l∞空间上的映射的零解延拓定理,再应用此定理证明了在耦合情况下当阻尼γ、外力h和频率ω满足ω2>3γ2,h21<h2<h22时,存在频率为ω的离散暗呼吸子.最后结合扰动算子的谱理论给出了其稳定性的理论证明.

This paper is devoted to the study of the existence and stability of discrete breathers of driven and damped DNLS equation in one-dimensional lattices.Instead of using the commonly used homoclinic orbit approach,which can not give the rigorous analysis,we frist study in detail the periodic solutions of the single oscillator.Then we apply the continuation theorem to the coupled DNLS equation and prove that when the damping force γ,driving force h and frequency ω satisfy ω^2〉3γ^2,h1^2〈h^2〈h2^2, a discrete dark breather with the fre quency ω exist. Last we show that the stability can be analyzed rigorously due to the detailed discussion of the single oscillator and the spectral theory of perturbation of operator.