Speaker:  Jacek Jendrej (CNRS and Universite Sorbonne Paris Nord)

Title:  Dynamics of kink clusters for scalar fields in dimension 1+1

Abstract:  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.