Quasi-Lie schemes: theory and applications

被引：16

作者：

Carinena, Jose F. ^{[1
]}

Grabowski, Janusz ^{[2
]}

de Lucas, Javier ^{[1
,2
]}

机构：

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

[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2009年 / 42卷 / 33期

关键词：

SUPERPOSITION RULES; 1ST INTEGRALS; EMDEN-FOWLER; SYSTEMS; EQUATION;

D O I：

10.1088/1751-8113/42/33/335206

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A powerful method to solve nonlinear first-order ordinary differential equations, which is based on a geometrical understanding of the corresponding dynamics of the so-called Lie systems, is developed. This method enables us not only to solve some of these equations, but also gives geometrical explanations for some, already known, ad hoc methods of dealing with such problems.

引用

页数：20

共 36 条

[1] GROUP THEORETICAL APPROACH TO SUPERPOSITION RULES FOR SYSTEMS OF RICCATI-EQUATIONS [J].

ANDERSON, RL ;

HARNAD, J ;

WINTERNITZ, P .

LETTERS IN MATHEMATICAL PHYSICS, 1981, 5 (02) :143-148

[2]

[Anonymous], 1931, Q. J. Math, DOI [10.1093/qmath/os-2.1.259, DOI 10.1093/QMATH/OS-2.1.259]

[3]

[Anonymous], 2000, Universitext

[4]

Berkovich L.M., 1997, Symmtry Nonlinear Math. Phys, V1, P155

[5]

Carinena J.F., 2007, 9 INT C DIFF GEOM AP, P437

[6] Integrability of the Riccati equation from a group-theoretical viewpoint [J].

Cariñena, JF ;

Ramos, A .

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1999, 14 (12) :1935-1951

[7] The nonlinear superposition principle and the Wei-Norman method [J].

Carinena, JF ;

Marmo, G ;

Nasarre, J .

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1998, 13 (21) :3601-3627

[8] A non-linear oscillator with quasi-harmonic behaviour:: two- and n-dimensional oscillators [J].

Cariñena, JF ;

Rañada, MF ;

Santander, M ;

Senthilvelan, M .

NONLINEARITY, 2004, 17 (05) :1941-1963

[9] Reduction of time-dependent systems admitting a superposition principle [J].

Cariñena, JF ;

Grabowski, J ;

Ramos, A .

ACTA APPLICANDAE MATHEMATICAE, 2001, 66 (01) :67-87

[10]

CARINENA JF, 2007, DIFFERENTIAL GEOMETR, P15

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