Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model
Roy Goodman. A Dynamical Perspective on the \(\varphi^4\) Model, Nonlinear Systems and Complexity 26 (Springer), 2019.
Abstract
We analyze the fractal structure seen in kink-antikink collisions of the \(\varphi^4\) equation. The analysis is based on qualitative ordinary differential equation models related to those obtained using the variational approximation. We derive a discrete-time iterated map approximation to the dynamics, from which many features of the model ODE system may be derived. We discuss the problems with Sugiyama’s variational model that have been pointed out recently by Takyi and Weigel.
Type
Publication
A Dynamical Perspective on the \(\varphi^4\) Model, Nonlinear Systems and Complexity 26 (Springer), 75–91
Authors
Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences
I am a professor in the Department of Mathematical Sciences at NJIT. My research applies methods of dynamical systems to (conservative, dispersive) nonlinear wave equations arising, for example, in optics and fluid mechanics. I am interested in dynamical and bifurcation phenomena, and I use techniques from Hamiltonian mechanics and perturbation theory, as well as extensive computations. My current research in vortex dynamics is supported by the NSF under DMS-2206016.
I led the effort to start the SIAM New York-New Jersey-Pennsylvania Section (SIAM NNP) and was its first president in 2023-2024. I have handed over the reins to a new leadership group.