Equações de Painlevé mistas e modelo PIII-PV simétrico

• Ano de defesa: 2015
• Autor(a) principal: Ruy, Danilo Virges [UNESP]
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual Paulista (Unesp)
• Palavras-chave em Português: Painlevé, Equações de; Teoria de campos; Backlund, Transformações de; Dirac, Equações de
• Link de acesso: http://hdl.handle.net/11449/124148; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/22-05-2015/000829086.pdf

This thesis studies the connection among integrable models and Painlev'e equations. We begin by extending the modified truncation approach in order to find B¨acklund transformations for the mKdV-Liouville hierarchy and its self-similarity reduction. With this method, we solve Kudryashov's conjecture partially. Then we study the extended mixed AKNS-Lund-Regge model and show this model can be reduced to PIV and PV equation for particular values of the parameters. We also construct the symmetric PIII-PV model in order to unify some cases of the PIII equation with the PV equation. After, we search for canonical constraints for reduce the 4-bose model to the symmetric PIII-PV model. For find the correct constraints, we construct the method of ansatz of constraints. In addition, we show a method for finding solutions for differential equations inD dimensions in the addendum. We also apply this method for the 'lâmbda'fi'POT.4 model