Oleksandr Chvartatskyi, Yuriy Sydorenko, “Darboux Transformations for <nobr>$(2+1)$</nobr>-Dimensional Extensions of the KP Hierarchy”, SIGMA, 2015, Volume 11,028, 20 pp.

This article is cited in 3 papers

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

Oleksandr Chvartatskyi^a, 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

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.

MSC: 35Q51; 35Q53; 35Q55; 37K35

Received: September 23, 2014; in final form March 27, 2015; Published online April 10, 2015

Language: English

DOI: 10.3842/SIGMA.2015.028