Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 002, 18 pages      arXiv:0811.0110      https://doi.org/10.3842/SIGMA.2009.002
Contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries

Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System

Aristophanes Dimakis a and Folkert Müller-Hoissen b
a) Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Str., GR-82100 Chios, Greece
b) Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Göttingen, Germany

Received November 01, 2008, in final form January 04, 2009; Published online January 08, 2009

Abstract
Via a Cole-Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole-Hopf transformation leads to a more general relation between the multicomponent linear heat hierarchy and the multicomponent KP hierarchy. From this results a construction of exact solutions of the latter via a matrix linear system.

Key words: multicomponent KP hierarchy; Burgers hierarchy; Cole-Hopf transformation; Davey-Stewartson equation; Riccati equation; dromion.

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