Geodesic
Dynamics of kink clusters for scalar fields in dimension 1+1
Jendrej, Jacek1 ; Lawrie, Andrew2
1 CNRS and LAGA (UMR 7539) Université Sorbonne Paris Nord 99 av Jean-Baptiste Clément 93430 Villetaneuse, France
2 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave, 2-267 Cambridge, MA 02139, U.S.A.
Journées équations aux dérivées partielles (2023), Exposé no. 7, 12 p.

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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.

The aim of this note is to expose some developments on asymptotic behaviour of kink clusters obtained in our recent preprint [23]. The results are partially inspired by the notion of “parabolic motions” in the Newtonian n-body problem. We present this analogy and mention its limitations. We also explain the role of kink clusters as universal profiles for formation of multi-kink configurations.

Publié le :
DOI : 10.5802/jedp.678
Classification : 35L71, 35B40, 37K40
Keywords: kink, multi-soliton, nonlinear wave

Jendrej, Jacek 1 ; Lawrie, Andrew 2

1 CNRS and LAGA (UMR 7539) Université Sorbonne Paris Nord 99 av Jean-Baptiste Clément 93430 Villetaneuse, France
2 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave, 2-267 Cambridge, MA 02139, U.S.A. 
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Jendrej, Jacek; Lawrie, Andrew. Dynamics of kink clusters for scalar fields in dimension $1+1$. Journées équations aux dérivées partielles (2023), Exposé no. 7, 12 p.. doi: 10.5802/jedp.678

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