Algorithmic construction of lumps
type: Item
instance of: scholarly article
title: Algorithmic construction of lumps
zbMATH Open document ID: 1144.82079
published in: Theoretical and Mathematical Physics
publication date: 2008-05-20T00:00:00Z
review text: This paper deals with the study of the Schrödinger-type system \(m_y+uw=iu_t+u_{xx}+2um_x=-iw_t+w_{xx}+2wm_x= 0\). The authors are interested to construct an algorithmic procedure based on the singular manifold method to generate rational solitons (lumps) for this class of systems. This method enables the authors to iterate fields, eigenfunctions, and singular manifolds such that new solutions arise iteratively from trivial seed solutions. Basic tools in the proofs are Darboux transformations and Lax pairs.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 82D55
Mathematics Subject Classification ID: 35Q51
zbMATH DE Number: 5277539
zbMATH Keywords: Lax pair
zbMATH Keywords: lump
zbMATH Keywords: Painlevé property
zbMATH Keywords: singular manifold
zbMATH Keywords: Darboux transformation
author: P. G. Estévez
author: J. Prada
MaRDI profile type: Publication
full work available at URL: s11232-007-0060-x
OpenAlex ID: W2156152872
cites work: The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
cites work: Q4657343
cites work: Darboux transformation and solutions for an equation in 2+1 dimensions
cites work: On the simplest integrable equation in 2+1
cites work: Some reductions of the self-dual Yang–Mills equations to integrable systems in 2+1 dimensions
cites work: The Kadomtsev–Petviashvili equation as a source of integrable model equations
cites work: Exotic coherent structures in the (2+1) dimensional long dispersive wave equation
cites work: Painlevé analysis of new higher-dimensional soliton equation
cites work: Integrable two-dimensional generalisation of the sine- and sinh-Gordon equations
cites work: Miura transformation between two non-linear equations in 2+1 dimensions
cites work: Darboux transformations via Painlevé analysis
DOI: 10.1007/S11232-007-0060-X
description: scientific article; zbMATH DE number 5277539