On the uniqueness of multi-breathers of the modified Korteweg–de Vries equation
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Alexander Semenov [1]
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[1] University of Strasbourg
University of Strasbourg
Arrondissement de Strasbourg-Ville, Francia
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 4, 2023, págs. 1247-1322
- Idioma: inglés
- DOI: 10.4171/RMI/1363
- Enlaces
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Resumen
We consider the modified Korteweg–de Vries equation, and prove that given any sum P of solitons and breathers (with distinct velocities), there exists a solution p such that p.t / P .t / ! 0 when t ! C1, which we call multi-breather. In order to do this, we work at the H2 level (even if usually solitons are considered at the H1 level). We will show that this convergence takes place in any Hs space and that this convergence is exponentially fast in time. We also show that the constructed multi-breather is unique in two cases: in the class of solutions which converge to the profile P faster than the inverse of a polynomial of a large enough degree in time (we will call this a super polynomial convergence), or when all the velocities are positive (without any hypothesis on the convergence rate).
