Título: Stability of Mkdv Breathers on The Half-Line
Palestrante: Márcio Cavalcante (UFAL)
Resumo: In this talk I will discuss the stability problem for mKdV breathers on the left half-line. We are able to show that leftwards moving breathers, initially located far away from the origin, are strongly stable for the problem posed on the left half-line, when assuming homogeneous boundary conditions. The proof involves a Lyapunov functional which is almost conserved by the mKdV flow once we control some boundary terms which naturally arise. Also, recent results about orbital and asymptotic stability of solitons on the positive half-line will be discussed. This is a joint work with Miguel Alejo and Adán Corcho.