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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
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
Citation:
Oleksandr Chvartatskyi, Yuriy Sydorenko, “Darboux Transformations for $(2+1)$-Dimensional Extensions of the KP Hierarchy”, SIGMA, 11 (2015), 028, 20 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1009 https://www.mathnet.ru/eng/sigma/v11/p28
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