Abstract
There is a long and rich story of nonlinear dynamics in discrete lattices. A particular well studied model is the discrete Nonlinear Schr\"odinger Equation, with many applications, most notably in nonlinear optics.
Recent studies have explored dynamics in scenarios where coupling amongst the array elements is nonlocal. The interest in particular is that in the longwave approximation, it leads to fractional diffraction. In this contribution, we consider two long range interaction lattice wave models, the fractional discrete nonlinear Schr\"odinger equation and the Long Range Ablowitz-Ladik system. By use of perturbation methods, asymptotics and numerical simulations, we present results on modulational instabilities, the emergence of coherent structures, mobility properties of localied modes, and a statistical mechanics framework for the formation of breathers.
Degree Date
Spring 5-17-2015
Document Type
Thesis
Degree Name
Ph.D.
Department
Computational & Applied Mathematics
Advisor
Alejandro Aceves
Number of Pages
94
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Marstaller, Austin E., "Nonlinear Phenomena of Discrete Wave Systems With Nonlocal Coupling" (2015). Mathematics Theses and Dissertations. 30.
https://scholar.smu.edu/hum_sci_mathematics_etds/30
