Equações de Painlevé mistas e modelo PIII-PV simétrico - Ruy, Danilo Virges [UNESP] (2015)
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