On a regularized full dispersion Davey-Stewartson system

Hung Luong; Jean-Claude Saut

doi:10.3934/dcds.2026116

Article Contents

2026, Volume 56: 557-578. Doi: 10.3934/dcds.2026116

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On a regularized full dispersion Davey-Stewartson system

Hung Luong^1, and
Jean-Claude Saut^2, ,

1.
Vietnam institute of Mathematics, VAST, 18B Hoang Quoc Viet, Nghia Do Ward, Ha Noi, Vietnam
2.
Laboratoire de Mathématiques, Université Paris-Saclay, Bâtiment 307, F-91405 Orsay, France

^*Corresponding author: Jean-Claude Saut
^*Corresponding author: Jean-Claude Saut

Received: March 24, 2026

Revised: June 3, 2026

Early access: June 12, 2026

Published online: June 12, 2026

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Abstract

This paper which continues [31] is concerned with the Cauchy problem for the full-dispersion Davey-Stewartson system introduced in [24]. More precisely, in order to invert the equation for the mean mode $ \phi $, we introduce an approximate system by a suitable truncation of the high frequencies of $ \phi $ and we prove that the solutions to the truncated systems converge to the solutions of the classical Davey-Stewartson system.

The paper starts with a survey on the derivation and known results on the Davey-Stewartson systems and their full-dispersion versions.

Keywords:

Wave propagation,
cauchy problem,
full dispersion Davey-Stewartson systems,
deep water models,
modulation equations.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 35Q55.

Citation:

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Figure 1. Dependence on $ |\textbf{K}|H_0 $ of the nonlinearity coefficient

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