Strongly interacting solitary waves for the fmKdV equation
A talk in the Oberseminar Analysis series by
Frederic Fernand Jacques Valet
| Abstract: | $\href{https://uni-bielefeld.zoom.us/j/98606776055?pwd=azBFdUVaQnJMU01tWjZUVEdxN2x5Zz09}{\textbf{Join Zoom Meeting}}$ Meeting-ID: 986 0677 6055 Passwort: 430747 The fractional modified Korteweg-de Vries equation : $∂_tu + ∂_x (|D|^αu + u^3) = 0$, for $α ∈ (1, 2)$ enjoys the existence of solitary waves : those solutions keep their form along the time and move with a constant velocity in one direction. Since the existence of multi-solitary waves with different velocities has been established (see [Eychenne 2021]), we are interested in constructing solutions behaving at large time as a sum of two solitary waves with the same velocity. I will first introduce the equation and the asymptotic behaviour of solitary waves, and state the existence of solutions whose asymptotic behaviour is a sum of two strongly interacting solitary waves with almost the same velocity. This is a joint work with Arnaud Eychenne. Within the CRC this talk is associated to the project(s): A1 |