Separation of variables and explicit theta-function solution of the classical Steklov--Lyapunov systems: A geometric and algebraic geometric background

2009/12/09 by Yu. V. Fedorov, Fedorov, Yuri, Inna Basak +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0912.1788

openalex publication_date 2009/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper revises the explicit integration of the classical Steklov--Lyapunov systems via separation of variables, which was first made by F. Kötter in 1900, but was not well understood until recently. We give a geometric interpretation of the separating variables and then, applying the Weierstrass hyperelliptic root functions, obtain explicit theta-function solution to the problem. We also analyze the structure of its poles on the corresponding Abelian variety. This enables us to obtain a solution for an alternative set of phase variables of the systems that has a specific compact form.

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