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

Symmetry Integrability and Geometry-Methods and Applications

article

Oleksandr Chvartatskyi¹  Yuriy Sydorenko² 

[1] Mathematisches Institut;Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv

关键词: KP hierarchy;    symmetry constraints;    binary Darboux transformation;    Davey– Stewartson equation;    KP equation with self-consistent sources;   

DOI  :  10.3842/SIGMA.2015.028

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown