On the derivative nonlinear Schrödinger equation

Nakao Hayashi, Tohru Ozawa

研究成果: Article査読

106 被引用数 (Scopus)

抄録

In this paper we discuss the Cauchy problem for the derivative nonlinear Schrödinger equation: i∂tψ + 2iδ∂x(|;ψ|2ψ) = 0, ψ(0, x) = f{cyrillic}(x), where δ ≠ 0. Under an explicit smallness condition of the initial data, we prove the unique global existence of solutions to this problem in the usual Sobolev spaces, in the weighted Sobolev spaces, and in the Schwartz class. We describe the smoothing effect in detail. Furthermore, for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction.

本文言語English
ページ(範囲)14-36
ページ数23
ジャーナルPhysica D: Nonlinear Phenomena
55
1-2
DOI
出版ステータスPublished - 1992 2
外部発表はい

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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