NJIT Applied Mathematics Colloquium
Friday, February 24, 2012, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology
Coherent Structures and Shocks in a Periodic Nonlinear Maxwell System
Gideon Simpson
University of Minnesota
The primitive
equations governing wave propagation in spatially varying optical
fibers are the nonlinear Maxwell equations, though these are often
reduced to the nonlinear coupled mode equations (NLCME). NLCME describes
the evolution of the slowly varying envelope of an appropriate carrier
wave. They are
known to possess solitons, which may be of use in optical transmission.
In
this talk, we numerically demonstrate the mathematical inconsistency
between NLCME and Maxwell, while still finding localized solutions for
prepared data. The inconsistency can be corrected through the inclusion
of infinitely many harmonics leading us to consider the extended
nonlinear coupled mode equations (xNLCME). This system introduces new
questions on the existence of localized states. Lastly, we consider
when a spatially varying index of refraction will be sufficient to
inhibit shock formation.
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