Stability of mKdV breathers on the half-line

Miguel A. Alejo (), Márcio Cavalcante () and Adán J. Corcho ()
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Miguel A. Alejo: Universidad de Córdoba
Márcio Cavalcante: Universidade Federal de Alagoas
Adán J. Corcho: Universidade Federal do Rio de Janeiro

Partial Differential Equations and Applications, 2022, vol. 3, issue 6, 1-21

Abstract: 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.

Keywords: Modified KdV equation; Breather solution; Cauchy Problem; Orbital stability; Half-line; Primary; 35Q55 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00209-9

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