标题： 通过显式公式为某些非局部和非线性可积偏微分方程设计谱准确的全离散格式 显示英文标题

标题： Spectrally accurate fully discrete schemes for some nonlocal and nonlinear integrable PDEs via explicit formulas

摘要： We construct fully-discrete schemes for the Benjamin-Ono, Calogero-Sutherland DNLS, and cubic Szegő equations on the torus, which are $\textit{exact in time}$ with $\textit{spectral accuracy}$ in space. We prove spectral convergence for the first two equations, of order $K^{-s+1}$ for initial data in $H^s(\mathbb T)$, with an error constant depending $\textit{linearly}$ on the final time instead of exponentially. These schemes are based on $\textit{explicit formulas}$, which have recently emerged in the theory of nonlinear integrable equations. Numerical simulations show the strength of the newly designed methods both at short and long time scales. These schemes open doors for the understanding of the long-time dynamics of integrable equations. 显示英文摘要

摘要： We construct fully-discrete schemes for the Benjamin-Ono, Calogero-Sutherland DNLS, and cubic Szeg\H{o} equations on the torus, which are $\textit{exact in time}$ with $\textit{spectral accuracy}$ in space. We prove spectral convergence for the first two equations, of order $K^{-s+1}$ for initial data in $H^s(\mathbb T)$, with an error constant depending $\textit{linearly}$ on the final time instead of exponentially. These schemes are based on $\textit{explicit formulas}$, which have recently emerged in the theory of nonlinear integrable equations. Numerical simulations show the strength of the newly designed methods both at short and long time scales. These schemes open doors for the understanding of the long-time dynamics of integrable equations.