The nonlinear Schrödinger limit and the initial layer of the Zakharov equations

Tohru Ozawa, Yoshio Tsutsumi, H. Brezis

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

We discuss the formation of the convergence of solutions for the Zakharov equations as the ion sound speed λ goes to infinity. We describe how the solutions tend to the corresponding solutions for the nonlinear Schrödinger equation and how the initial layer phenomena occur. A clear account is given of the relation between the convergence rate in λ and the formation of the initial layers.

Original languageEnglish (US)
Pages (from-to)721-745
Number of pages25
JournalDifferential and Integral Equations
Volume5
Issue number4
StatePublished - Jan 1 1992

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Convergence of Solutions
Nonlinear equations
Convergence Rate
Nonlinear Equations
Infinity
Acoustic waves
Tend
Ions
Sound

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "We discuss the formation of the convergence of solutions for the Zakharov equations as the ion sound speed λ goes to infinity. We describe how the solutions tend to the corresponding solutions for the nonlinear Schr{\"o}dinger equation and how the initial layer phenomena occur. A clear account is given of the relation between the convergence rate in λ and the formation of the initial layers.",
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The nonlinear Schrödinger limit and the initial layer of the Zakharov equations. / Ozawa, Tohru; Tsutsumi, Yoshio; Brezis, H.

In: Differential and Integral Equations, Vol. 5, No. 4, 01.01.1992, p. 721-745.

Research output: Contribution to journalArticle

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AU - Brezis, H.

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N2 - We discuss the formation of the convergence of solutions for the Zakharov equations as the ion sound speed λ goes to infinity. We describe how the solutions tend to the corresponding solutions for the nonlinear Schrödinger equation and how the initial layer phenomena occur. A clear account is given of the relation between the convergence rate in λ and the formation of the initial layers.

AB - We discuss the formation of the convergence of solutions for the Zakharov equations as the ion sound speed λ goes to infinity. We describe how the solutions tend to the corresponding solutions for the nonlinear Schrödinger equation and how the initial layer phenomena occur. A clear account is given of the relation between the convergence rate in λ and the formation of the initial layers.

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