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SIGMA 11 (2015), 028, 20 pages arXiv:1409.5444
https://doi.org/10.3842/SIGMA.2015.028
Darboux Transformations for $(2+1)$-Dimensional Extensions of the KP Hierarchy
Oleksandr Chvartatskyi a and Yuriy Sydorenko b
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
Received September 23, 2014, in final form March 27, 2015; Published online April 10, 2015
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.
Key words:
KP hierarchy; symmetry constraints; binary Darboux transformation; Davey-Stewartson equation; KP equation with self-consistent sources.
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