Local well-posedness for the KdV hierarchy at high regularity

TL;DR

This paper establishes well-posedness results in high-regularity Sobolev spaces for a broad class of nonlinear higher-order dispersive equations extending the KdV hierarchy, applicable on both the line and torus.

Contribution

It provides the first high-regularity well-posedness results for a general class of higher-order KdV-type equations on different domains.

Findings

Well-posedness in $H^s$ for high $s$ for KdV hierarchy generalizations.

Applicable to equations on both the line and the torus.

Extends previous results to higher-order dispersive equations.

Abstract

We prove well-posedness in $L^2$-based Sobolev spaces $H^s$ at high regularity for a class of nonlinear higher-order dispersive equations generalizing the KdV hierarchy both on the line and on the torus.