Complex Behavior in Coupled Nonlinear Waveguides
Abstract
We consider the nonlinear propagation of light along an array of two or three coupled waveguides. The three waveguide system is known to support nine different stationary time-harmonic solutions. We consider the relative periodic orbits that occur due to some bifurcations in this system, including Hamiltonian Hopf bifurcations and saddle-node (\(0^2i\omega\)) bifurcations.
Date
Nov 1, 2016 2:00 PM
Event
Location
Institute for Mathematics and Applications
University of Minnesota, Minneapolis, MN
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.