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A Bäcklund transformation and nonlinear superposition formula for the Lotka-Volterra hierarchy

Published online by Cambridge University Press:  17 February 2009

Xing-Biao Hu  and
Johan Springael
Xing-Biao Hu
Affiliation:
Academy of Mathematics and Systems Sciences, State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific Engineering Computing, Academia Sinica, P.O. Box 2719, Beijing 100080, P.R. China; e-mail: [email protected]. Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury CT2 7NF, United Kingdom.
Johan Springael
Affiliation:
Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium; e-mail: [email protected].
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Abstract

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A hierarchy of bilinear Lotka-Volterra equations with a unified structure is proposed. The bilinear Bäcklund transformation for this hierarchy and the corresponding canonical Lax pair are obtained. Furthermore, the nonlinear superposition formula is proved rigorously.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 121 - 128
Copyright
Copyright © Australian Mathematical Society 2002

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