Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions

Daniella Bekiranov, Takayoshi Ogawa, Gustavo Ponce

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

An interaction equation of the capillary-gravity wave is considered. We show that the Cauchy problem of the coupled Schrödinger-KdV equation, (itu + x2u -αvu + γ|u|2u, x ∈ R, tv + x3 + xv2x(|u|2), u(x, 0) = u0(x), v(x, 0) = v0(x), is locally well-posed for weak initial data U0 × v0 ε L2(R) × L21/2(R) × H-1/2 (R). We apply the analogous method for estimating the nonlinear coupling terms developed by Bourgain and refined by Kenig, Ponce, and Vega.

Original languageEnglish
Pages (from-to)2907-2919
Number of pages13
JournalProceedings of the American Mathematical Society
Volume125
Issue number10
DOIs
Publication statusPublished - 1997
Externally publishedYes

Keywords

  • Capillary-gravity wave
  • Kdv
  • Nonlinear Schrödinger
  • Well-posedness

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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