KdV-type equations in projective Gevrey classes

TL;DR

This paper establishes well-posedness results for a class of third order quasilinear evolution equations, including KdV-type equations, within projective Gevrey spaces, linking mathematical physics models with advanced functional analysis.

Contribution

It introduces a novel well-posedness framework for KdV-type equations in projective Gevrey classes, extending previous results to more general variable coefficient cases.

Findings

Proved well-posedness for a broad class of third order equations

Connected the analysis to equations in mathematical physics

Extended the theory to variable coefficient scenarios

Abstract

We prove well-posedness of the Cauchy problem for a class of third order quasilinear evolution equations with variable coefficients in projective Gevrey spaces. The class considered is connected with several equations in Mathematical Physics as the KdV and KdVB equation and some of their many generalizations.