In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in Muñoz (Proyecciones (Antofagasta) 36(4):653–683, 2017), in the sense that a suitable modification of the Stokes wave is the global attractor of the local Akhmediev dynamics for sufficiently large time, and therefore the latter cannot be stable in any suitable finite energy periodic Sobolev space.
The Akhmediev breather is unstable / Alejo, M. A.; Fanelli, L.; Munoz, C.. - In: SÃO PAULO JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1982-6907. - 13:2(2019), pp. 391-401. [10.1007/s40863-019-00145-4]
The Akhmediev breather is unstable
Fanelli L.;
2019
Abstract
In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in Muñoz (Proyecciones (Antofagasta) 36(4):653–683, 2017), in the sense that a suitable modification of the Stokes wave is the global attractor of the local Akhmediev dynamics for sufficiently large time, and therefore the latter cannot be stable in any suitable finite energy periodic Sobolev space.File allegati a questo prodotto
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