Autor(es)

Alves, V. C. C. ; Aratyn, H. ; Gomes, J. F. ; Zimerman, A. H. ; IOP

• Tipo de documento: Artigo Científico
• Fonte: WAKE CONFERENCE 2021; v. 1194, p. 9-pg., 2019-01-01.

Resumo

The paper discusses PIII-V equation for special values of its parameters for which this equation reduces to P-III, I-12, as well as, to some special cases of I-38 and I-49 equations from the Ince's list of 50 second order differential equations possessing Painleve property. These reductions also yield symmetries governing the reduced models obtained from the PIII-V equation. We point out that the solvable equations on Ince's list emerge in this reduction scheme when the underlying reflections of the Weyl symmetry group no longer include an affine reflection through the hyperplane orthogonal to the highest root and therefore do not give rise to an affine Weyl group. We hypothesize that on the level of the underlying algebra and geometry this might be a fundamental feature that distinguishes the six Painleve equations from the remaining 44 solvable equations on the Ince's list. (AU)

• Processo FAPESP: 16/22122-9 - Sistema Integrável de 6-bósons/ Hierarquias Integráveis na Rede
• Beneficiário: Victor César Costa Alves
• Modalidade de apoio: Bolsas no Brasil - Doutorado