Original Articles

A NOTE ON FIRST INTEGRALS AND LAX REPRESENTATION

Published in: Quaestiones Mathematicae
Volume 11 , issue 3 , 1988 , pages: 301–305

DOI: 10.1080/16073606.1988.9632146

Author(s): W.-H. Steeb Department of Applied Mathematics and Nonlinear Studies Rand Afrikaans, South Africa , A.J. van Tonder Department of Applied Mathematics and Nonlinear Studies Rand Afrikaans, South Africa

Keywords: 34A34 , 22370

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Abstract

Let du_i/dt = F_i(u) (i = 1, …, n) be a scale invariant autonomous system of first order ordinary differential equations, where the F_i's are polynomials. The following question will be discussed: Assume that du_i/dt = F_i(u) admits a Lax representation. Does the Lax representation provide all the first integrals of the dynamical system? By means of a counter example we show that this is not generally the case.

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