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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 …
Rogue Waves In Nonlinear Schrodinger Models With Variable Coefficients : Application To Bose Einstein Condensates, J. S. He, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskasis
Rogue Waves In Nonlinear Schrodinger Models With Variable Coefficients : Application To Bose Einstein Condensates, J. S. He, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskasis
Mathematics and Statistics Department Faculty Publication Series
We explore the form of rogue waves solution sin a select set of case examples of non linear Schrodinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue waves solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations …
Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis
Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
In this work, we consider the dynamics of vector rogue waves and ark bright solitons in two component nonlinear Schrodinger equations with various physically motivated time dependent non linearity coefficients, as well as spatio temporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark bright boomeron like soliton solutions of the latter are converted back into ones of the original non autonomous model. Using direct numerical simulations we find that, in most cases, the rogue waves formation is rapidly followed by a modulational instability that leads …
Lattice Three Dimensional Skyrmions Revisited, E. G. Charalampidis, T. A. I, P. G. Kevrekidis
Lattice Three Dimensional Skyrmions Revisited, E. G. Charalampidis, T. A. I, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, an a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the three dimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed: and their stability under small perturbation sis explored by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, …