SYMMETRIES AND SOLUTIONS OF A THIRD ORDER EQUATION

Autor(es)

Sampaio, Julio Cesar Santos ^[1] ; Freire, Igor Leite ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed ABC UFABC, Ctr Matemat Comp & Cognicao, Rua Santa Adelia 166, BR-09 :2101 Santo Andre, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; n. SI, p. 981-989, 2015.
• Citações Web of Science: 0

Resumo

In this paper we study a new third order evolution equation discovered a couple of years ago using a genetic programming. We show that the Lie symmetries of this equation corresponds to space and time translations, as well as a dilation on the space of independent variables and another one with respect to the depend variable. From its symmetries, explicit solutions of the equation are obtained, some of them expressed in terms of the solutions of the Airy equation and Abel equation of the second kind. Additionally, by using the direct method we establish three conservation laws for the equation, one of them new. (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