Numerical study of Davey-Stewartson I systems

2021/09/19 by Jörg Frauendiener, Christian Klein, Frauendiener, J. +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2109.09169

openalex publication_date 2021/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An efficient high precision hybrid numerical approach for integrable Davey-Stewartson (DS) I equations for trivial boundary conditions at infinity is presented for Schwartz class initial data. The code is used for a detailed numerical study of DS I solutions in this class. Localized stationary solutions are constructed and shown to be unstable against dispersion and blow-up. A finite-time blow-up of initial data in the Schwartz class of smooth rapidly decreasing functions is discussed.

Citations

• On three-dimensional packets of surface waves

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