On the complete integrability and linearization of nonlinear ordinary differential equations. III. Coupled first-order equations

被引:13
作者
Chandrasekar, V. K. [1 ]
Senthilvelan, M. [1 ]
Lakshmanan, M. [1 ]
机构
[1] Bharathidasan Univ, Dept Phys, Ctr Nonlinear Dynam, Tiruchirappalli 620024, India
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2009年 / 465卷 / 2102期
关键词
nonlinear differential equations; coupled first order; integrability; integrating factor; linearization; 1ST INTEGRALS; DARBOUX INTEGRABILITY;
D O I
10.1098/rspa.2008.0239
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Continuing our study on the complete integrability of nonlinear ordinary differential equations (ODEs), in this paper we consider the integrability of a system of coupled first-order nonlinear ODEs of both autonomous and non-autonomous types. For this purpose, we modify the original Prelle-Singer (PS) procedure so as to apply it to both autonomous and non-autonomous systems of coupled first-order ODEs. We briefly explain the method of finding integrals of motion (time-independent as well as time-dependent integrals) for two and three coupled first-order ODEs by extending the PS method. From this we try to answer some of the open questions in the original PS method. We also identify integrable cases for the two-dimensional Lotka-Volterra system and three-dimensional Rossler system as well as other examples including non-autonomous systems in a straightforward way using this procedure. Finally, we develop a linearization procedure for coupled first-order ODEs.
引用
收藏
页码:585 / 608
页数:24
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