Darboux transformations for higher-rank Kadomtsev-Petviashvili and Krichever-Novikov equations
type: Item
instance of: scholarly article
title: Darboux transformations for higher-rank Kadomtsev-Petviashvili and Krichever-Novikov equations
zbMATH Open document ID: 0840.35096
DOI: 10.1007/BF00994646
author: G. A. Latham
author: Emma Previato
published in: Acta Applicandae Mathematicae
publication date: 1995-08-27T00:00:00Z
review text: The work is devoted to further applications of the algebraic geometry techniques to finding exact solutions for the Kadomtsev-Petviashvili (KP) equation. It is shown that a special Darboux transformation, called transference, acting on a pair of commuting differential operators of orders 4 and 6, implements the Abelian sum on their joint elliptic spectrum. Those transformations map KP solutions into solutions to the so-called Krichever-Novikov equations, which can be further mapped, by another transformation belonging to the same class, into solutions to the Korteweg-de Vries (KdV) equation. Reversing the sequence of the two mappings, one can construct exact solutions to the KP solutions, starting from those for the KdV equation. As an example, it is shown how a rational nondecaying solution to the KdV equation generates rational KP solutions.
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 790810
zbMATH Keywords: transference
zbMATH Keywords: algebro-geometric solutions
zbMATH Keywords: Kadomtsev-Petviashvili equation
zbMATH Keywords: exact solutions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00994646
OpenAlex ID: W4242260263
description: scientific article; zbMATH DE number 790810