On the radius of analyticity of solutions to the cubic Szegő equation

This paper is concerned with the cubic Szegő equationi∂tu=Π(|u|2u),i∂tu=Π(|u|2u), defined on the L2L2 Hardy space on the one-dimensional torus TT, where Π:L2(T)→L+2(T) is the Szegő projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time t∈(−∞,∞)t∈(−∞,∞). In addition, we find a lower bound for the radius of analyticity of the solution. Our method involves energy-like estimates of the special Gevrey class of analytic functions based on the ℓ1ℓ1 norm of Fourier transforms (the Wiener algebra).