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

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• 作者：Artur Sergyeyev ^{Artur.Sergyeyev@math.slu.cz}
• 关键词：Coupling constant metamorphosis ; Generalized Stä ; ckel transform ; Integrable systems ; Integrals of motion ; Symmetries ; Lax pairs
• 刊名：Physics Letters A
• 出版年：2012
• 期刊代码：57_03759601
• 类别：ph
• 出版时间：4 June, 2012
• 卷：376
• 期：28-29
• 页码：2015-2022
• 文件大小：215 K

摘要

In the present Letter we extend the multiparameter coupling constant metamorphosis, also known as the generalized St盲ckel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This transform interchanges the values of integrals of motion with the parameters these integrals depend on but leaves the phase space coordinates intact. Sufficient conditions under which the transformation in question preserves integrability and a simple formula relating the solutions of the original system to those of the transformed one are given.