# Numerical Study of Blowup in the Davey-Stewartson System

@article{Klein2011NumericalSO, title={Numerical Study of Blowup in the Davey-Stewartson System}, author={Christian Klein and Benson K. Muite and K. Roidot}, journal={arXiv: Analysis of PDEs}, year={2011} }

Nonlinear dispersive partial differential equations such as the nonlinear Schr\"odinger equations can have solutions that blow-up. We numerically study the long time behavior and potential blowup of solutions to the focusing Davey-Stewartson II equation by analyzing perturbations of the lump and the Ozawa exact solutions. It is shown in this way that the lump is unstable to both blowup and dispersion, and that blowup in the Ozawa solution is generic.

## 20 Citations

### Numerical Study of Blow‐Up Mechanisms for Davey–Stewartson II Systems

- Mathematics
- 2017

We present a detailed numerical study of various blow‐up issues in the context of the focusing Davey–Stewartson II equation. To this end, we study Gaussian initial data and perturbations of the lump…

### Numerical study of Davey–Stewartson I systems

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- 2022

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…

### A NUMERICAL APPROACH TO BLOW-UP ISSUES FOR DAVEY-STEWARTSON II SYSTEMS

- Mathematics
- 2015

. We provide a numerical study of various issues pertaining to the dynamics of the Davey-Stewartson II systems. In particular we investigate whether or not the properties (blow-up, radiation,...)…

### A numerical approach to Blow-up issues for Davey-Stewartson II type systems

- Mathematics
- 2014

We provide a numerical study of various issues pertaining to the dynamics of the Davey-Stewartson systems of the DS II type. In particular we investigate whether or not the properties (blow-up,…

### Soliton solutions and their (in)stability for the focusing Davey–Stewartson II equation

- MathematicsNonlinearity
- 2018

We give a rigorous mathematical analysis of the one-soliton solution of the focusing Davey–Stewartson II equation and a proof of its instability under perturbation. Building on the fundamental…

### Parallel Computing for the study of the focusing Davey-Stewartson II equation in semiclassical limit

- Mathematics
- 2012

The asymptotic description of the semiclassical limit of nonlinear Schrodinger equations is a major challenge with so far only scattered results in 1 + 1 dimensions. In this limit, solutions to the…

### On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2019

We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schrödinger type and…

### Remarks on the full dispersion Davey-Stewartson systems

- Mathematics
- 2015

We consider the Cauchy problem for the Full Dispersion Davey-Stewartson systems derived in [23] for the modeling of surface water waves in the modulation regime and we investigate some of their…

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