Remarks on nonlinear Schrödinger equations in one space dimension

Nakao Hayashi, Tohru Ozawa, J. L. Bona

Research output: Contribution to journalArticle

81 Citations (Scopus)

Abstract

We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥

Original languageEnglish
Pages (from-to)453-461
Number of pages9
JournalDifferential and Integral Equations
Volume7
Issue number2
Publication statusPublished - 1994
Externally publishedYes

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Initial value problems
Local Solution
Nonlinear equations
Initial Value Problem
Nonlinear Equations
Polynomials
Polynomial
Term

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Remarks on nonlinear Schrödinger equations in one space dimension. / Hayashi, Nakao; Ozawa, Tohru; Bona, J. L.

In: Differential and Integral Equations, Vol. 7, No. 2, 1994, p. 453-461.

Research output: Contribution to journalArticle

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