Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 045, 18 pages      arXiv:1811.09096      https://doi.org/10.3842/SIGMA.2019.045

Lax Representations for Separable Systems from Benenti Class

Maciej Błaszak a and Ziemowit Domański b
a) Faculty of Physics, Division of Mathematical Physics, A. Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland
b) Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

Received December 13, 2018, in final form June 07, 2019; Published online June 18, 2019

Abstract
In this paper we construct Lax pairs for Stäckel systems with separation curves from so-called Benenti class. For each system of considered family we present an infinite family of Lax representations, parameterized by smooth functions of spectral parameter.

Key words: Lax representation; Stäckel system; Benenti system; Hamiltonian mechanics.

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