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Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials
Non-square lattices, Nonlinear waves Photonic lattices
2014/12/8
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
An O(N) Method for Rapidly Computing Periodic Potentials Using Accelerated Cartesian Expansions
Accelerated Cartesian Expansion (ACE) Fast Multipole Methods Periodic Systems
2011/10/8
Abstract: The evaluation of long-range potentials in periodic, many-body systems arises as a necessary step in the numerical modeling of a multitude of interesting physical problems. Direct evaluation...
Exact solutions of the modified Gross-Pitaevskii equation in `smart' periodic potentials in the presence of external source
exact solutions modified Gross-Pitaevskii equation
2010/4/6
We report wide class of exact solutions of the modified Gross-Pitaevskii equation (GPE) in `smart' Jacobi elliptic potentials: $V(\xi)=-V_{0}{\rm sn(\xi,m)}$, $V(\xi)=-V_{0}{\rm cn(\xi,m)}$, and $V(\x...