Power series solution of the modified KdV equation

TL;DR

This paper establishes local well-posedness for the modified KdV equation in Fourier-Lebesgue spaces using a novel method by M. Christ, advancing the understanding of solutions in these function spaces.

Contribution

It introduces a new approach to prove well-posedness of the mKdV equation in Fourier-Lebesgue spaces, extending previous results.

Findings

Proves local well-posedness in $\

Uses M. Christ's method for the analysis

Extends the class of initial data for which mKdV solutions are known

Abstract

We prove local-wellposedness of the mKdV equation in $\mathcal{F}L^{s,p}$ spaces using the new method of M. Christ.