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Full-Text Articles in Physical Sciences and Mathematics
Dark-Bright Solitons And Vortices In Bose-Einstein Condensates, Dong Yan
Dark-Bright Solitons And Vortices In Bose-Einstein Condensates, Dong Yan
Doctoral Dissertations
This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrodinger equation, the so-called Gross-Pitaevskii (GP) equation, which is a mean-field description of BECs. The systematic analysis begins by considering the dark-bright (DB)-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component BECs. The interaction between two DB solitons in a homogeneous condensate and at the presence of the trap are both considered. Our analytical approximation relies in a Hamiltonian perturbation theory, which leads to an equation of motion of the centers of DB-soliton interacting pairs. Employing this equation, we demonstrate the …
Discrete Parity-Time Symmetric Nonlinear Schrodinger Lattices, Kai Li
Discrete Parity-Time Symmetric Nonlinear Schrodinger Lattices, Kai Li
Doctoral Dissertations
In this thesis we summarize the classical cases of one-dimensional oligomers and two dimensional plaquettes, respecting the parity-time (PT ) symmetry. We examine different types of solutions of such configurations with linear and nonlinear gain or loss profiles. For each configuration, we develop a dynamical model and examine its PT symmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient, γ. Once the relevant waveforms have been identified (analytically or numerically), their stability as well as those of the ghost states in certain regimes is examined by means of linearization …