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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 002, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.002 (Mi sigma348) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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

Aristophanes Dimakisa, Folkert Müller-Hoissenb

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
Full-text PDF (608 kB) Citations (3)
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DOI: https://doi.org/10.3842/SIGMA.2009.002
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.
Keywords: multicomponent KP hierarchy; Burgers hierarchy; Cole–Hopf transformation; Davey–Stewartson equation; Riccati equation; dromion.
Received: November 1, 2008; in final form January 4, 2009; Published online January 8, 2009
Bibliographic databases:
Document Type: Article
MSC: 37K10; 35Q53
Language: English
Citation: Aristophanes Dimakis, Folkert Müller-Hoissen, “Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System”, SIGMA, 5 (2009), 002, 18 pp.
Citation in format AMSBIB
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\by Aristophanes Dimakis, Folkert M\"uller-Hoissen
\paper Multicomponent Burgers and KP Hierarchies, and Solutions from a~Matrix Linear System
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\vol 5
\papernumber 002
\totalpages 18
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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