ENERGY CASCADE FOR THE KLEIN-GORDON LATTICE

被引：0

作者：

Pasquali, Stefano ^{[1
,2
]}

机构：

[1] Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France

[2] Int Sch Adv Studies SISSA, Via Bonomea 265, I-34136 Trieste, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年 / 45卷 / 06期

基金：

欧盟地平线“2020”;

关键词：

Klein-Gordon lattice; continuous approximation; energy cascade; weak turbulence; nonlinear Schrodinger equation; SOBOLEV NORMS; DIFFUSION; DYNAMICS; GROWTH; METASTABILITY; OSCILLATIONS; EQUATION; NLS;

D O I：

10.3934/dcds.2024149

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study analytically the dynamics of a d-dimensional Klein- Gordon lattice with periodic boundary conditions, for d <= 3 . We consider initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation, the resonant normal form of the system is given by a small-dispersion nonlinear Schrodinger (NLS) equation. By exploiting a result about the growth of Sobolev norms for solutions of the small-dispersion NLS equation, we are able to describe an energy cascade phenomenon for the Klein-Gordon lattice, where part of the energy is transferred to modes associated to higher frequencies. Such a phenomenon holds within the time-scale for which we can ensure the validity of the continuous approximation.

引用

页码：1823 / 1869

页数：47

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