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
收藏
页码：683 / 699
页数：17
相关论文
共 29 条
[1]   Effective mass Schrodinger equation for exactly solvable class of one-dimensional potentials [J].
Aktas, Metin ;
Sever, Ramazan .
JOURNAL OF MATHEMATICAL CHEMISTRY, 2008, 43 (01) :92-100
[2]  
BERKOVICH LM, 1982, FUNCT ANAL APPL+, V16, P190
[3]  
BRAZIER TI, 1994, REV MEX FIS, V40, P378
[4]  
Carinena J., 2000, LIE SCHEFFERS SYSTEM
[5]   A new geometric approach to Lie systems and physical applications [J].
Cariñena, JF ;
Ramos, A .
ACTA APPLICANDAE MATHEMATICAE, 2002, 70 (1-3) :43-69
[6]  
CARINENA JF, 2007, DIFFERENTIAL GEOMETR, P15
[7]   Recent Applications of the Theory of Lie Systems in Ermakov Systems [J].
Carinena, Jose F. ;
De Lucas, Javier ;
Ranada, Manuel F. .
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2008, 4
[8]   A nonlinear superposition rule for solutions of the Milne-Pinney equation [J].
Carinena, Jose F. ;
de Lucas, Javier .
PHYSICS LETTERS A, 2008, 372 (33) :5385-5389
[9]   Superposition rules, lie theorem, and partial differential equations [J].
Carinena, Jose F. ;
Grabowski, Janusz ;
Marmo, Giuseppe .
REPORTS ON MATHEMATICAL PHYSICS, 2007, 60 (02) :237-258
[10]   Quasi-Lie schemes: theory and applications [J].
Carinena, Jose F. ;
Grabowski, Janusz ;
de Lucas, Javier .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (33)
123