- Series
- PDE Seminar
- Time
- Tuesday, November 7, 2023 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Jacek Jendrej – CNRS and LAGA, Universite Sorbonne Paris Nord – jendrej@math.univ-paris13.fr – https://www.math.univ-paris13.fr/~jendrej/
- Organizer
- Gong Chen
We consider classical scalar fields in dimension 1+1 with a
self-interaction potential being a symmetric double-well. Such a model
admits non-trivial static solutions called kinks and antikinks. A kink
cluster is a solution approaching, for large positive times, a
superposition of alternating kinks and antikinks whose velocities
converge to 0 and mutual distances grow to infinity. Our main result is
a determination of the asymptotic behaviour of any kink cluster at the
leading order.
Our results are partially inspired by the notion of "parabolic motions"
in the Newtonian n-body problem. I will present this analogy and mention
its limitations. I will also explain the role of kink clusters as
universal profiles for formation of multi-kink configurations.
This is a joint work with Andrew Lawrie.