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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
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DOI: https://doi.org/10.3842/SIGMA.2015.028
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
MSC: 35Q51; 35Q53; 35Q55; 37K35
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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