event
Monday 14 Nov 2011: Maths seminar - Variational approximations to homoclinic snakings in continuous and discrete systems
Hadi Susanto - University of Nottingham
Harrison 203 15:00-16:00
In this talk, we will present our study on the snaking of localised patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, that are not accessible via standard multiple-scales asymptotic techniques, yet it is considerably simpler than an exponential asymptotic method. We apply the method in particular to the quadratic and the cubic Swift-Hohenberg equations and the discrete Allen-Cahn equation. Using the variational formulation, we obtain the symmetric snaking solutions and the asymmetric 'ladder' states, and predict the stability of the states. We will show that the resulting approximate formulas for the width of the snaking region is in good agreement with numerical results.
