Local and nonlocal solvable structures in the reduction of ODEs

被引:26
作者
Ferraioli, D. Catalano [1 ]
Morando, P. [2 ]
机构
[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy
[2] Univ Milan, Ist Ingn Agr, Fac Agr, I-20133 Milan, Italy
基金
英国工程与自然科学研究理事会;
关键词
ORDINARY DIFFERENTIAL-EQUATIONS; LAMBDA-SYMMETRIES; MU-SYMMETRIES; GEOMETRY;
D O I
10.1088/1751-8113/42/3/035210
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ordinary differential equations (ODEs) by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice, a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure.
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页数:15
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