Soliton dynamics in frequency-modulated lattices

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Copyright: Sun, Yang
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Abstract
Currently, experimental and theoretical studies of solitons have been conducted in the context of several areas of science, from applied mathematics and physics to chemistry and biology. A significant amount of soliton research is concentrated on nonlinear optics (light waves) and Bose-Einstein condensates (matter waves) in optical lattices, which are often described by the Gross-Pitaevskii equation or the nonlinear Schrodinger equation with a periodic potential. We studied soliton dynamics in both time-independent and time-dependent potentials. We used a variational approach to simplify the problem by reducing it to the study of the dynamics of a particle in an effective potential. We saw good agreement between the numerical and approximate variational solutions, indicat- ing the variational method is a simple yet powerful method for the study of soliton dynamics in a frequency-modulated potential. We studied several scenarios, includ- ing soliton trapping by a periodic potential, â jumpingâ between adjacent wells and parametric resonance. We also investigated the soliton dynamics by using Poincar´e sections and histograms to examine the velocity distribution of the driven solitons for different initial conditions.
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Author(s)
Sun, Yang
Supervisor(s)
Alexander, Tristram
Jovanoski, Zlatko
Towers, Isaac
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Publication Year
2014
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Thesis
Degree Type
Masters Thesis
UNSW Faculty
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