The Cubic Szegő Equation on the Real Line: Explicit Formula and Well-Posedness on the Hardy Class

We establish an explicit formula for the solution of the cubic Szeg & odblac; equation on the real line. Using this formula, we prove that the evolution flow of this equation can be continuously extended to the whole Hardy class H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>2$$\end{document} on the real line.