The second Hamiltonian structure for a special case of the Lotka-Volterra equations

被引：0
|
作者：
Bibik Yu.V. [1 ]
机构：
[1] Computing Center, Russian Academy of Sciences, Moscow 119991
来源：
Computational Mathematics and Mathematical Physics | 2007年 / 47卷 / 8期
基金：
俄罗斯基础研究基金会;
关键词：
Hamiltonian structure; Integrability by quadratures; Lotka-Volterra equations;
D O I：
10.1134/S0965542507080064
中图分类号：
学科分类号：
摘要：
A special case of the Lotka-Volterra equations is considered for which it is possible to find the second Hamiltonian structure that is complementary to the known one. The form of the new Hamiltonian makes it possible to solve the equations by quadratures, which is the main feature of the case under examination. As a consequence, the period can also be represented by quadratures. In terms of the new variables, the equations of motion admit a mechanical analogy with the oscillations of a mass on a nonlinear spring. © 2007 Pleiades Publishing, Ltd.
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页码：1285 / 1294
页数：9
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