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

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Author(s):
Figueira, Renata O. ; Panthee, Mahendra
Total Authors: 2
Document type: Journal article
Source: JOURNAL OF EVOLUTION EQUATIONS; v. 24, n. 2, p. 24-pg., 2024-06-01.
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 Schrodinger 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. (AU)

FAPESP's process: 23/06416-6 - Nonlinear phenomena and dispersion
Grantee:Mahendra Prasad Panthee
Support Opportunities: Regular Research Grants
FAPESP's process: 21/04999-9 - Evolution of the radius of analyticity for dispersive equations and systems involving them
Grantee:Renata de Oliveira Figueira
Support Opportunities: Scholarships in Brazil - Post-Doctoral