On the numerical evaluation of algebro-geometric solutions to integrable equations
type: Item
instance of: scholarly article
title: On the numerical evaluation of algebro-geometric solutions to integrable equations
zbMATH Open document ID: 1251.37067
DOI: 10.1088/0951-7715/25/3/569
published in: Nonlinearity
publication date: 2012-05-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1107.2108
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 6030677
zbMATH Keywords: integrable partial differential equations
zbMATH Keywords: theta functions
zbMATH Keywords: real Riemann surfaces
MaRDI profile type: Publication
OpenAlex ID: W3103597506
arXiv ID: 1107.2108
author: C. Kalla
author: C. Klein
review text: The authors address typical analytical problems appearing in the numerical study of theta-functional solutions to integrable PDEs and present the state of the art of the field by considering concrete examples. They first recall some basic facts from the theory of multi-dimensional theta functions and the theory of real Riemann surfaces, necessary to give theta-functional solutions to the n-NLS (nonlinear Schrödinger) and DS (Davey-Stewartson) equations. Then, the authors consider the hyperelliptic case and study concrete examples of low genus, also in almost degenerate situations. They also consider examples of non-hyperelliptic real Riemann surfaces and discuss symplectic transformations needed to obtain smooth solutions. The paper concludes with some remarks.
reviewed by: Ahmed Lesfari
description: scientific article; zbMATH DE number 6030677