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Эта публикация цитируется в 25 научных статьях (всего в 25 статьях)
Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations
Concepción Muriel, Juan Luis Romero Department of Mathematics, University of Cádiz, 11510 Puerto Real, Spain
Аннотация:
This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of $\lambda$-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the $\lambda$-coverings method. The $\lambda$-symmetry approach let us characterize the nonlocal symmetries that are useful to reduce the order and provides an alternative method of computation that involves less unknowns. The notion of equivalent $\lambda$-symmetries is used to decide whether or not reductions associated to two nonlocal symmetries are strictly different.
Ключевые слова:
nonlocal symmetries; $\lambda$-symmetries; telescopic vector fields; order reductions; differential invariants.
Поступила: 9 июля 2012 г.; в окончательном варианте 19 декабря 2012 г.; опубликована 28 декабря 2012 г.
Образец цитирования:
Concepción Muriel, Juan Luis Romero, “Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations”, SIGMA, 8 (2012), 106, 21 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma783 https://www.mathnet.ru/rus/sigma/v8/p106
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