681	RWTH Publication No: 1003622        2024
TITLE	Spectrally accurate fully discrete schemes for some nonlocal and nonlinear integrable PDEs via explicit formulas
AUTHORS	Yvonne Alama Bronsard, Xi Chen, Matthieu Dolbeault
ABSTRACT	We construct fully-discrete schemes for the Benjamin-Ono, Calogero-Sutherland DNLS, and cubic Szegő equations on the torus, which are exact in time with spectral accuracy in space. We prove spectral convergence for the first two equations, of order K−s+1 for initial data in Hs(T), with an error constant depending linearly on the final time instead of exponentially. These schemes are based on 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.
KEYWORDS	Integrable systems, Benjamin-Ono equation, explicit formulas, Lax pairs, spectral accuracy, fully discrete error analysis, long-time dynamics