| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | IMA JOURNAL OF APPLIED MATHEMATICS; v. 80, n. 6, p. 1739-1758, DEC 2015. |
| Web of Science Citations: | 3 |
| Abstract | |
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) | |
| FAPESP's process: | 12/22725-4 - Invariance properties and conserved quantities: Noether's theorem and Ibragimov's theorem |
| Grantee: | Priscila Leal da Silva |
| Support Opportunities: | Scholarships in Brazil - Master |
| FAPESP's process: | 14/05024-8 - Symmetries and conservation laws for differential equations arising from physical and biological systems |
| Grantee: | Igor Leite Freire |
| Support Opportunities: | Regular Research Grants |