On the Asymptotic Stability of Solitary Wave Solutions to the Boussinesq Model in the Energy Space.

Abstract: The Good Boussinesq (GB) model is known to admit solitary wave solutions with speeds in the range −1<c<1. In this talk, we revisit existing results and present new findings on the asymptotic stability of solitary wave solutions to the GB equation with power-type nonlinearity and general initial data in the energy space H1xL2.

These new result complete the orbital stability stability result established by Bona and Sachs (1988). The proof employs a novel set of virial estimates specifically tailored to the GB system in a moving frame. In particular, we introduce a mixed-variable virial estimate that effectively addresses arbitrary scaling and shift modulations. This is joint work with Claudio Muñoz.

Posted on Jan 9, 2025 in Differential Equations, Seminars