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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 028, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.028
(Mi sigma1009)
 

This article is cited in 3 scientific papers (total in 3 papers)

Darboux Transformations for $(2+1)$-Dimensional Extensions of the KP Hierarchy

Oleksandr Chvartatskyia, Yuriy Sydorenkob

a Mathematisches Institut, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
b Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine
Full-text PDF (440 kB) Citations (3)
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Abstract: New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of $(2+1)$-dimensional integrable equations, including the DS-III equation and the $N$-wave problem. Furthermore, we recover a system that contains two types of the KP equation with self-consistent sources as special cases. Darboux and binary Darboux transformations are applied to generate solutions of the proposed hierarchies.
Keywords: KP hierarchy; symmetry constraints; binary Darboux transformation; Davey–Stewartson equation; KP equation with self-consistent sources.
Received: September 23, 2014; in final form March 27, 2015; Published online April 10, 2015
Bibliographic databases:
Document Type: Article
Language: English
Citation: Oleksandr Chvartatskyi, Yuriy Sydorenko, “Darboux Transformations for $(2+1)$-Dimensional Extensions of the KP Hierarchy”, SIGMA, 11 (2015), 028, 20 pp.
Citation in format AMSBIB
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\by Oleksandr~Chvartatskyi, Yuriy~Sydorenko
\paper Darboux Transformations for $(2+1)$-Dimensional Extensions of the KP Hierarchy
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\papernumber 028
\totalpages 20
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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