Improved lower bound for the radius of analyticity for the modified KdV equation

2024/06/12 by Renata O. Figueira, Figueira, Renata O., Mahendra Panthee +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2406.08400

openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the initial value problem (IVP) associated to the modified Korteweg-de Vries equation (mKdV) in the defocusing scenario: \∂_t u+ ∂_x³u-u²∂_x(u) = 0, x,t∈ℝ,
u(x,0) = u₀(x),. where u is a real valued function and the initial data u₀ is analytic on ℝ and has uniform radius of analyticity σ₀ in the spatial variable. It is well-known that the solution u preserves its analyticity with the same radius σ₀ for at least some time span 0

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