Stability of mKdV breathers on the half-line

2022/06/06 by Miguel Á. Alejo, Alejo, Miguel A., Márcio André Araújo Cavalcante +3 · 1 citation
Engineering · Mathematics · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.02898

openalex publication_date 2022/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we study the stability problem for mKdV breathers on the left half-line. We are able to show that leftwards moving breathers, initially located far away from the origin, are strongly stable for the problem posed on the left half-line, when assuming homogeneous boundary conditions. The proof involves a Lyapunov functional which is almost conserved by the mKdV flow once we control some boundary terms which naturally arise.

Cited by

• On the Propagation of Regularity of Solutions to the KdV Equation on the positive Half-line

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