Estudo de soluções localizadas na equação não linear de Schrödinger logarítmica, saturada e com efeitos de altas ordens
Nenhuma Miniatura disponível
Data
2018-06-07
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal de Goiás
Resumo
This work presents the study of solitary wave solutions, known as solitons, in non-linear and non-
homogeneous media using non-linear Schrödinger equations. Three cases are studied: first
considering a logarithmic nonlinear term; second with saturation effect and finally including effects
of high orders (Raman scattering). Solutions are modulated by three different types of potential.
First, linear in the spatial and oscillatory coordinate in the temporal coordinate. The second,
quadratic in the spatial and oscillatory in the temporal coordinates. Finally, it is also modulated
using a mixed potential, which is the junction of the two potentials presented above. After including
inomogeneities in linear and nonlinear coefficients, the similarity transformation technique is used
to convert the non-linear, non-autonomous equation into an autonomous one that will be solved
analytically. This field of study has potential applications in crystals, optical fibers and in Bose-
Einstein condensates, also serving to understand the fundamentals related to this state of matter.
The stability of the solutions are checked by numerical simulations.
Descrição
Citação
CALAÇA, L. Estudo de soluções localizadas na equação não linear de Schrödinger logarítmica, saturada e com efeitos de altas ordens. 2018. 55 f. Tese (Doutorado em Física) - Universidade Federal de Goiás, Goiânia, 2018.