UC Davis Mathematics

Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Strongly interacting kink-antikink pairs for scalar fields on a line

PDE and Applied Math Seminar

Speaker: Jacek Jendrej, Université Paris 13
Related Webpage: https://www.math.univ-paris13.fr/~jendrej/
Location: MSB 2112
Start time: Thu, Jan 9 2020, 4:30PM

I will present a recent joint work with Michał Kowalczyk (Univ. de Chile) and Andrew Lawrie (MIT). A nonlinear wave equation with a double-well potential in 1+1 dimension admits stationary solutions called kinks and antikinks, which are minimal energy solutions connecting the two minima of the potential. We study solutions whose energy is equal to twice the energy of a kink, which is the threshold energy for a formation of a kink-antikink pair. We prove that, up to translations in space and time, there is exactly one kink-antikink pair having this threshold energy. I will explain the main ingredients of the proof.