APPLICATIONS OF LIE SYSTEMS IN DISSIPATIVE MILNE-PINNEY EQUATIONS

被引：29

作者：

Carinena, Jose F. ^{[1
]}

De Lucas, Javier ^{[1
]}

机构：

[1] Univ Zaragoza, Dept Fis Teor, E-50009 Zaragoza, Spain

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2009年 / 6卷 / 04期

关键词：

Superposition rule; Milne-Pinney equation; Ermakov system; quasi-Lie scheme; DIFFERENTIAL-EQUATIONS; HARMONIC-OSCILLATOR; GEOMETRIC APPROACH; INVARIANTS; TRANSFORMATION; THEOREM; ERMAKOV;

D O I：

10.1142/S0219887809003758

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express the general solution of a dissipative Milne-Pinney equation in terms of particular solutions of a system of second-order linear differential equations and a set of constants.

引用

页码：683 / 699

页数：17

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