Integrable nonlinear oscillators with N degrees of freedom: a constructive approach

被引：0

作者：

Ballesteros, Angel ^{[1
]}

Blasco, Alfonso ^{[1
]}

机构：

[1] Univ Burgos, Dept Fis, Burgos 09001, Spain

来源：

MATHEMATICS AND ASTRONOMY: A JOINT LONG JOURNEY | 2010年 / 1283卷

关键词：

nonlinear oscillator; perturbations; integrable systems; Lie algebras; coalgebras; Casimir functions; N-dimensional; HAMILTONIAN-SYSTEMS; QUARTIC POTENTIALS; SUPERINTEGRABILITY; SEARCH; SPACES; ORDER;

D O I：

10.1063/1.3506070

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

A constructive method to obtain integrable Hamiltonians with N degrees of freedom is presented. This approach is based on the h(6) Poisson coalgebra and allows us to construct two new families of nonlinear integrable perturbations of the N-dimensional oscillator. The first one is a family of integrable perturbations depending on N parameters and two arbitrary functions, and it includes as particular cases several known quartic and sextic coupled nonlinear oscillators. The second type of integrable perturbations contains homogeneous functions with degree -2 in the coordinates together with an arbitrary radial function. In all the cases, the integrals of the motion are explicitly given.

引用

页码：268 / 277

页数：10

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