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

par Jacek Jendrej

mardi 19 mars 2024, 15:15 → 16:15 Europe/Paris

Fokko du Cloux (Bâtiment Braconnier, La Doua)

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.