Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs

Details Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs

2010-08-09

arxiv.org/abs/1008.1575v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, LaTeX

Scientific paper

In the present paper we extend the coupling constant metamorphosis, also known as the (multiparameter generalized) St\"ackel transform, originally introduced for Hamiltonian dynamical systems, to general finite-dimensional dynamical systems and ODEs. Roughly speaking, the transformation in question interchanges the values of integrals of motion with the parameters that these integrals contain but leaves the phase space coordinates intact. Sufficient conditions under which the said transformation preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given.

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