BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrew Lawrie (University of Maryland\, College Park) DTSTART:20250227T163000Z DTEND:20250227T173000Z DTSTAMP:20260423T040039Z UID:SIAM-PDE/52 DESCRIPTION:Title: Soliton dynamics for classical scalar fields\nby Andrew Lawrie (Univ ersity of Maryland\, College Park) as part of Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nI will present some of my recent work with Jacek Jendrej. We study classical scalar fields in dimension 1+1 with a symmetric double-well self-interaction potential. Examples of such equations are the phi-4 model and the sine-Gordon equation. These nonline ar wave equations admit non-trivial static solutions called kinks and anti kinks\, which are amongst the simplest examples of topological solitons. W e define an n-kink cluster to be a solution approaching\, for large positi ve times\, a superposition of n alternating kinks and antikinks whose velo cities converge to zero and mutual distances grow to infinity. Our main re sult is a determination of the leading order asymptotic behavior of any n- kink cluster. We use this information to construct the n-dimensional invar iant manifold of n-kink clusters\, which plays the dynamical role of the s table/unstable manifold for an ideal "critical point at infinity” given by well separated multi-kink configurations. In this context we also expla in the role of kink clusters as universal profiles for the formation/annih ilation of multikink configurations.\n\nSession Chair: Atanas Stefanov\, U niversity of Alabama\, Birminghan (stefanov@uab.edu)\n LOCATION:https://researchseminars.org/talk/SIAM-PDE/52/ END:VEVENT END:VCALENDAR