The cubic Szeg\H{o} equation on the real line: explicit formula and well-posedness on the Hardy class

TL;DR

This paper derives an explicit solution formula for the cubic Szeg ext{"o} equation on the real line and demonstrates its well-posedness on the Hardy class $H^2$, extending the flow continuously.

Contribution

It provides the first explicit solution formula for the cubic Szeg ext{"o} equation on the real line and proves well-posedness on the Hardy class.

Findings

Explicit solution formula for the cubic Szeg ext{"o} equation on the real line

Continuous extension of the flow to the Hardy class $H^2$

Well-posedness of the equation on the Hardy class

Abstract

We establish an explicit formula for the solution of the the cubic Szeg\H{o} 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 $H^2$ on the real line.