The Euler-Jacobi-Lie integrability theorem

被引：29
作者：
Kozlov, Valery V. [1 ]
机构：
[1] Russian Acad Sci, VA Steklov Math Inst, Moscow 119991, Russia
来源：
REGULAR & CHAOTIC DYNAMICS | 2013年 / 18卷 / 04期
关键词：
symmetry field; integral invariant; nilpotent group; magnetic hydrodynamics; NONHOLONOMIC SYSTEMS; EXPLICIT INTEGRATION; INVARIANT-MANIFOLDS; SYMMETRY; FLOWS;
D O I：
10.1134/S1560354713040011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper addresses a class of problems associated with the conditions for exact integrability of systems of ordinary differential equations expressed in terms of the properties of tensor invariants. The general theorem of integrability of the system of n differential equations is proved, which admits n - 2 independent symmetry fields and an invariant volume n-form (integral invariant). General results are applied to the study of steady motions of a continuum with infinite conductivity.
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页码：329 / 343
页数：15
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