On hybrid Painleve equations

Autor(es)

Victor Cesar Costa Alves

• Tipo de documento: Tese de Doutorado
• Imprenta: São Paulo. 2021-06-22.
• Instituição: Universidade Estadual Paulista (Unesp). Instituto de Física Teórica (IFT). São Paulo
• Data de defesa: 2021-02-23
• Orientador: Abraham Hirsz Zimerman

Resumo

The theory of Painleve equations is first explained in the historical context of the creation of new equations from the singularity analysis on the complex plane. The study of the SL(N) mKdV hierarchy results in the theory of either the A(1) Painleve equations or the Ince’s equations, and naturally their Backlund Transformations for the corresponding reductions (coalescence). The theory of coalescence is then fully explored connecting all Ince's and Painleve equations. With such a formalism, we are able to construct hybrid equations that preserve the Painleve property. Going beyond that, deformed equations are then developed, extending the mixed equations. (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