Analytic solutions to nonelliptic nonlinear Schrödinger equations
type: Item
instance of: scholarly article
title: Analytic solutions to nonelliptic nonlinear Schrödinger equations
zbMATH Open document ID: 0798.35138
author: A. de Bouard
published in: Journal of Differential Equations
publication date: 1993-10-25T00:00:00Z
review text: This paper proves the existence of solutions holomorphic in the space variables, defined for small times, for a general class of equations including the Boussinesq equation and more sophisticated water-wave model equations (some of them involving a Hilbert transform) due to Dysthe and Hogan. The solutions are analytic in a strip which, in general, may shrink to zero width in finite time. These results generalize two papers of \textit{N. Hayashi} [SIAM J. Math. Anal. 22, No. 6, 1738--1743 (1991; Zbl 0742.35056) and Duke Math. J. 60, No. 3, 717--727 (1990; Zbl 0721.35026)] and the proofs involve similar techniques.
reviewed by: Satyanad Kichenassamy
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 76B15
zbMATH DE Number: 431286
zbMATH Keywords: water-wave models
zbMATH Keywords: holomorphic solutions
zbMATH Keywords: NLS-like equations
MaRDI profile type: Publication
full work available at URL: jdeq.1993.1069
OpenAlex ID: W2090214734
DOI: 10.1006/JDEQ.1993.1069
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description: scientific article; zbMATH DE number 431286