Nonlinear Waves from Beaches to Photonics

SpeakerDr. Mark Ablowitz
Organization University of Colorado
LocationEBII 1230
DateJanuary 17, 2014 12:50 PM

 Abstract:

The study of localized waves has a long history dating back to the discoveries in the 1800s describing solitary water waves in shallow water. In the 1960s researchers found that certain equations, such as the Korteweg-deVries (KdV) and nonlinear Schrodinger (NLS) equations arise widely. Both equations admit localized solitary wave--or soliton solutions. Employing a nonlocal formulation of water waves interesting asymptotic reductions of water waves are obtained. Some solutions will be discussed as well as how they relate to ocean observations. In the study of photonic lattices with simple periodic potentials, discrete and continuous NLS equations arise. In non-simple periodic, hexagonal or honeycomb lattices, novel discrete Dirac-like systems and their continuous analogs can be derived. They are found to have interesting properties. Since honeycomb lattices occur in the material graphene, the optical case is termed photonic graphene.

Bio:

Dr. Mark Ablowitz is a professor and the department chair of Applied Mathematics at the University of Colorado at Boulder. He received his BS in Mechanical Engineering from the University of Rochester and his PhD in Mathematics from MIT. He has received numerous honors throughout his career including the Alfred P. Sloan Foundation Fellowship and the John Simon Guggenheim Foundation Fellowship. He has more than 230 journal publications and has authored five books. His principal research interests include nonlinear phenomena and physical applied mathematics. 

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