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

• Autor(a) principal: Fabrício Cristófani
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Estadual de Maringá (RI-UEM)
• Texto Completo: http://repositorio.uem.br:8080/jspui/handle/1/5533
• topic: Estabilidade orbital; Ondas viajantes periódicas; Equação de Kawahara; Equação logarítima de Korteweg-de Vries; Equação dispersiva regularizada; Orbital stability; Periodic traveling waves; Kawahara equation; Logarithmic Korteweg-de Vries equation; Regularized dispersive equation; Ciências Exatas e da Terra; Matemática

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