Essential variables in the integrability problem of planar vector fields

被引：15

作者：

Gine, Jaume ^{[1
]}

Santallusia, Xavier ^{[1
]}

机构：

[1] Univ Lleida, Dept Matemat, Lleida 25001, Spain

来源：

PHYSICS LETTERS A | 2011年 / 375卷 / 03期

关键词：

Integrability problem; Systems of nonlinear differential equations; First integral; POINCARE-LIAPUNOV CONSTANTS; 2-DIMENSIONAL FLOWS; QUADRATIC SYSTEMS; 1ST INTEGRALS; C-2; CENTERS; POINTS;

D O I：

10.1016/j.physleta.2010.11.026

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This Letter is devoted to the integrability problem of planar nonlinear differential equations. We introduce a new method to detect local analytic integrability or to construct a singular series expansion of the first integral around a singular point for planar vector fields. The method allows to find new variables (essential variables) where the integrability problem is more feasible. The new method can be used in different context and is an alternative to all the methods developed up to now for any particular case. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：291 / 297

页数：7

共 29 条

[1] The integrability problem for a class of planar systems [J].