David McLaren
Publications:
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van der Kamp P. H., McLaren D. I., Quispel G. R. W.
On a Quadratic Poisson Algebra and Integrable Lotka – Volterra Systems with Solutions in Terms of Lambert’s $W$ Function
2025, vol. 30, no. 3, pp. 382-407
Abstract
We study a class of integrable inhomogeneous Lotka – Volterra systems whose
quadratic terms are defined by an antisymmetric matrix and whose linear terms consist
of three blocks. We provide the Poisson algebra of their Darboux polynomials and prove
a contraction theorem. We then use these results to classify the systems according to the
number of functionally independent (and, for some, commuting) integrals. We also establish
separability/solvability by quadratures, given the solutions to the 2- and 3-dimensional systems,
which we provide in terms of the Lambert $W$ function.
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