### 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 language | English |
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Pages (from-to) | 721-745 |

Number of pages | 25 |

Journal | Differential and Integral Equations |

Volume | 5 |

Issue number | 4 |

Publication status | Published - 1992 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Differential and Integral Equations*,

*5*(4), 721-745.

**The nonlinear Schrödinger limit and the initial layer of the Zakharov equations.** / Ozawa, Tohru; Tsutsumi, Yoshio; Brezis, H.

Research output: Contribution to journal › Article

*Differential and Integral Equations*, vol. 5, no. 4, pp. 721-745.

}

TY - JOUR

T1 - The nonlinear Schrödinger limit and the initial layer of the Zakharov equations

AU - Ozawa, Tohru

AU - Tsutsumi, Yoshio

AU - Brezis, H.

PY - 1992

Y1 - 1992

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.

UR - http://www.scopus.com/inward/record.url?scp=84972498389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972498389&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 721

EP - 745

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 4

ER -