Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrodinger equation

• 成果类型: Article
• 署名作者: Buckmaster, T.; Germain, P.; Hani, Z.; Shatah, J.
• 署名单位: Princeton University; University of Michigan System; University of Michigan
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01039-z
• 发表日期: 2021
• 页码: 787-855
• 关键词: continuous resonant equation; quantum boltzmann-equation; linear energy transfer; derivation; diffusion; EVOLUTION; spectrum; nls

摘要

Consider the cubic nonlinear Schrodinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation, predicted in wave turbulence theory, on a nontrivial timescale.