Estabilidade orbital de ondas viajantes periódicas para equações do tipo Korteweg-de Vries e dispersiva regularizada

Abstract

This thesis concerns the study of orbital stability of periodic traveling waves related for three important nonlinear dispersive equations. Initially, we study the orbital stability with dnoidal pro_le associated to the Kwahara equation based on the arguments developed in [7] and [13]. After, motivated by [28], we determine a global well-posedness result as well as the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. To do so, we have presented a smooth surface of periodic waves by using an improvement of the theory in [63]. The same work was used to establish the spectral properties of the linearized operator around the periodic wave. Next, an adaptation of the stablity theories developed in [45], [54] and [79] were presented to get our stability results. Final, we showed a new criterion to obtain the orbital stability of periodic traveling waves related to a general class of regularized dispersive equations. The study is based on the recent ideas from [6] and it has, as a direct application of our method, the fact that a special class of regularized fractionary Korteweg-de Vries equations always admit stable periodic waves