The prolongation structures of quasi-polynomial flows
- 8 February 1983
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 385 (1789) , 389-429
- https://doi.org/10.1098/rspa.1983.0020
Abstract
We look closely at the process of finding a Wahlquist-Estabrook prolongation structure for a given (system of) nonlinear evolution equation(s). There are two main steps in this calculation: the first, to reduce the problem to the investigation of a finitely generated, free Lie algebra with constraints; the second, to find a finite-dimensional linear representation of these generators. We discuss some of the difficulties that arise in this calculation. For quasi-polynomial flows (defined later) we give an algorithm for the first step. We do not totally solve the problems of the second step, but do give an algebraic framework and a number of techniques that are quite generally applicable. We illustrate these methods with many examples, several of which are new.Keywords
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