Nonlinear Dynamics of Bloch Wave Packets in Honeycomb Lattices

Mark J. Ablowitz Department of Applied Mathematics, University of Colorado, 526 UCB, Boulder, CO 80309-0526, USA Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China

TBD mathscidoc:2204.43023

Nonlinear waves in deformed optical honeycomb lattices are investigated. Discrete couple mode equations are used to find higher order continuous nonlinear Dirac systems which are employed to describe key underlying phenomena. For weak deformation and nonlinearity the wave propagation is circular–ellliptical. At strong nonlinearity the diffraction pattern becomes triangular in structure which is traced to appropriate nonequal energy propagation in momentum space. At suitably large deformation the dispersion structure can have nearby Dirac points or small gaps. The effective dynamics of the wave packets is described by two maximally balanced nonlocal nonlinear Schrödinger type equations.
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  title={Nonlinear Dynamics of Bloch Wave Packets in Honeycomb Lattices},
  author={Mark J. Ablowitz, and Yi Zhu},
Mark J. Ablowitz, and Yi Zhu. Nonlinear Dynamics of Bloch Wave Packets in Honeycomb Lattices. 2013.
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