Well-posedness for the Schrödinger-Korteweg-de Vries system

By A. Corcho, Felipe Linares. 2007

64 citations recorded by the source corpus.

We study well-posedness of the Cauchy problem associated to the Schrodinger-Korteweg-de Vries system. We obtain local well-posedness for weak initial data, where the best result obtained is for data in the Sobolev space L 2 (R) x H -3 4+ . This result implies in particular the global well-posedness in the energy space H 1 (R) x H 1 (R). Both results considerably improve the previous ones by Bekiranov, Ogawa and Ponce (1997), Guo and Miao (1999), and Tsutsumi (1993).

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6950bf260e0ec019d39addb6f186afb1aca4ac61

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Citations in the corpus

• Existence and Stability of a Two-Parameter Family of Solitary Waves for an NLS-KdV System (2012, background): “In the case when p = 1 and q = 2, for arbitrary values of τ1, τ2, and α, this problem has been shown to be well-posed locally in time by Bekiranov et al. in [5], and global wellposedness was proved by Corcho and Linares [9].”