Symmetry analysis of a class of autonomous even-order ordinary differential equations

Autor(es)

da Silva, Priscila Leal ^[1] ; Freire, Igor Leite ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Programa Posgrad Matemat, BR-09210580 Santo Andre, SP - Brazil

^[2] Univ Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210580 Santo Andre, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IMA JOURNAL OF APPLIED MATHEMATICS; v. 80, n. 6, p. 1739-1758, DEC 2015.
• Citações Web of Science: 3

Resumo

A class of autonomous, even-order ordinary differential equations is discussed from the point of view of Lie symmetries. It is shown that for a certain power non-linearity, the Noether symmetry group coincides with the Lie point symmetry group. First integrals are established and exact solutions are found. Furthermore, this paper complements, for the one-dimensional case, some results in the literature of Lie group analysis of poliharmonic equations and Noether symmetries obtained in the last 20 years. In particular, it is shown that the exceptional negative power discovered in Bokhari et al. (2010, Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation. J. Math. Phys., 51, 053517) is a member of a one-parameter family of exceptional powers in which the Lie symmetry group coincides with the Noether symmetry group. (AU)

• Processo FAPESP: 12/22725-4 - Propriedades de invariância e quantidades conservadas: o Teorema de Noether e o Teorema de Ibragimov
• Beneficiário: Priscila Leal da Silva
• Modalidade de apoio: Bolsas no Brasil - Mestrado
• Processo FAPESP: 14/05024-8 - Simetrias e leis de conservação de equações diferenciais oriundas de sistemas físicos e biológicos
• Beneficiário: Igor Leite Freire
• Modalidade de apoio: Auxílio à Pesquisa - Regular