New lower bounds for the radius of analyticity for the mKdV equation and a system of mKdV-type equations

Abstract

This paper is devoted to obtaining new lower bounds to the radius of spatial analyticity for the solutions of modified Korteweg–de Vries (mKdV) equation and a coupled system of mKdV-type equations, starting with real analytic initial data with a fixed radius of analyticity \(\sigma _0\). Specifically, we derive almost conserved quantities to prove that the local solution can be extended to a time interval [0, T] for any large \(T>0\) in such a way that the radius of analyticity \(\sigma (T)\) decays no faster than \(cT^{-1}\) for both the equations, where c is a positive constant. The results of this paper improve the ones obtained in Figueira and Panthee (Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion, to appear in NoDEA, arXiv:2307.09096) and Figueira and Himonas (J Math Anal Appl 497(2):124917, 2021), respectively, for the mKdV equation and a mKdV-type system.