Low regularity conservation laws for integrable PDE

TL;DR

This paper introduces a unified method to derive conservation laws for integrable PDEs at negative regularity, applicable to KdV, NLS, and mKdV equations on both line and circle.

Contribution

A novel, general approach for negative regularity conservation laws in integrable PDEs, extending previous methods to multiple equations and domains.

Findings

Successfully derived conservation laws for KdV, NLS, and mKdV at negative regularity.

Applicable to equations on both the line and circle.

Provides a unified framework for these PDEs.

Abstract

We present a general method for obtaining conservation laws for integrable PDE at negative regularity and exhibit its application to KdV, NLS, and mKdV. Our method works uniformly for these problems posed both on the line and on the circle.