Numerical study of Davey-Stewartson I systems

TL;DR

This paper presents a high-precision hybrid numerical method for solving Davey-Stewartson I equations, investigates the stability of solutions, and discusses finite-time blow-up phenomena for smooth initial data.

Contribution

It introduces a novel hybrid numerical approach for DS I equations and provides detailed numerical analysis of solution stability and blow-up behavior.

Findings

Localized stationary solutions are unstable against dispersion and blow-up.

Finite-time blow-up occurs for smooth rapidly decreasing initial data.

The numerical method achieves high precision for Schwartz class initial data.

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.