Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Variational Methods for Evolving Objects, L. Ambrosio, Y. Giga, P. Rybka and Y. Tonegawa, eds. (Tokyo: Mathematical Society of Japan, 2015), 157 - 224
Dynamics of topological defects in nonlinear field theories
We survey recent results that characterize the dynamics, in a certain asymptotic limit, of interfaces in certain semilinear hyperbolic equations, as well as vortex filaments in semilinear hyperbolic systems. This survey includes a lengthy discussion of heuristic considerations, together with some complete proofs in simple model cases. We also present some novel recent approaches to problem that geometric evolution problem of timelike extremal submanifolds of Minkowski space, which governs the asymptotic dynamics of interfaces and vortex filaments.
Received: 26 March 2013
Revised: 4 July 2013
First available in Project Euclid: 19 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L71: Semilinear second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions
Jerrard, Robert L. Dynamics of topological defects in nonlinear field theories. Variational Methods for Evolving Objects, 157--224, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06710157. https://projecteuclid.org/euclid.aspm/1539916037