# Programa de Pós-graduação em Física

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### Navegando Programa de Pós-graduação em Física por Por Orientador "Cardoso, Wesley Bueno"

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Item Estudo de soluções localizadas na equação não linear de Schrödinger logarítmica, saturada e com efeitos de altas ordens(Universidade Federal de Goiás, 2018-06-07) Alves, Luciano Calaça; Avelar, Ardiley Torres; http://lattes.cnpq.br/5732286631137637; Cardoso, Wesley Bueno; http://lattes.cnpq.br/6845416823133684; Bazeia Filho, Dionisio; Valverde, Clodoaldo; Santana, Ricardo Costa de; Maia, Lauro June QueirozMostrar mais 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.Mostrar mais Item Dinâmica e decaimento de sólitons escuros em condensados de Bose-Einstein atômicos quase-unidimensionais(Universidade Federal de Goiás, 2014-02-25) Couto, Hugo Leonardo Carvalhaes; Cardoso, Wesley Bueno; Cardoso, Wesley Bueno; Losano, Laercio; Avelar, Ardiley TorresMostrar mais (Sem resumo em outra língua)Mostrar mais Item Método compacto de diferenças finitas para resolver equações de Schrödinger não lineares com dispersão de quarta ordem(Universidade Federal de Goiás, 2016-09-16) Jesus, Hugo Naves; Cardoso, Wesley Bueno; http://lattes.cnpq.br/6845416823133684; Cardoso, Wesley Bueno; http://lattes.cnpq.br/6845416823133684; Avelar, Ardiley Torres; Bazeia, Dionisio; Mendanha Neto, Sebastião AntônioMostrar mais Finite difference schemes belong to a class of numerical methods used to approximate derivatives. They are widely used to find approximations to differential equations. There are a lot of numerical methods, whose deductions are made through expansions in Taylor Series. Depending on the manner in which expansion is made, it can be combined with other expansions to obtain derivatives with better numerical approximations. Usually when we get numerical derivative with better approaches, it is necessary to increase the amount of points used in the grid. An alternative to this problem are compact methods, which achieve better approximations for the same derivative but without increasing the number of mesh points. This work is an attempt to develop the Compact-SSFD method for the Schrödinger Equation Nonlinear Fourth Order. SSFD methods are used to separate the parts of a differential equation so that each part can be solved separately. For example in the case of non-linear differential equations it is often used to separate the linear parts of nonlinear parts. In Compact-SSFD methods nonlinear parts are resolved exactly as the linear are resolved using compact methods. Our work is inspired in the Dehghan and Taleei’s work where was used the Compact-SSFD method for solving numerically the equation Nonlinear Schrödinger. Before we try to develop our method, the results of the authors was correctly reproduced. But when we try to deduce a method analogous to the differential equation we wanted to solve, which also involves derived from fourth order, we realized that a Compact type method does not get as trivially as in the case of used to approach second-order derivatives.Mostrar mais Item Redução dimensional para condensados de Bose-Einstein em forma de “tubo” e “anilha plana”(Universidade Federal de Goiás, 2019-02-28) Santos, Mateus Calixto Pereira dos; Cardoso, Wesley Bueno; http://lattes.cnpq.br/6845416823133684; Cardoso, Wesley Bueno; Avelar, Ardiley Torres; Santana, Ademir Eugênio deMostrar mais The study of nonlinear dynamics represents a challenge of contemporary physics. In particular, the investigation of Bose Einstein condensates proved to be a hard task due to the large number of interacting particles. Therefore, given the difficulty of modeling these systems, approximations were introduced, which promoted the description of the Bose-Einstein condensation state in interacting atomic gases as a three-dimensional nonlinear Schrödinger equation, known as the Gross-Pitaevskii equation. In this work we review the dimensional reduction method, which use a variational treatment with the goal of derive effective one-dimensional (1D) and two-dimensional (2D) equations in cigar-shaped and pancake-shaped Bose-Einstein condensates, where we show that these equations describe almost exactly the dynamics of their respective models. Thus, we studied the ground-state solutions in tube-shaped and flat washer-shaped Bose-Einstein condensates by means of effectives non-polynomials equations, derived from the dimensional reduction method. The results produced by this equations were in very good agreement with those obtained from the corresponding full 3D Gross-Pitaevskii equation.Mostrar mais Item Espalhamento de gaussons em acopladores ópticos direcionais(Universidade Federal de Goiás, 2017-04-10) Teixeira, Rafael Marques Paes; Cardoso, Wesley Bueno; http://lattes.cnpq.br/6845416823133684; Avelar, Ardiley Torres; Ramos, Jorge Gabriel Gomes de SouzaMostrar mais This dissertation presents the research that was focused on the study of solitons in nonintegrable systems governed by effective models of partial differential equations (PDEs) of (1+1) dimensions, that is, one spatial and one time dimension. In the main research line, we considered a model of two fields given by nonlinear Schrödinger equations with logarithmic nonlinearity and linear coupling, the main aspects of the collision dynamics of two Gaussian solitons (gaussons) were investigated, addressing the stability of the solutions, the interaction mechanisms, and the regularity of the scattering. The study of gaussons collisions in this model was performed via two approaches: semianalytic (variational/reduced model) and direct numerical simulation. For the system considered in this work, both approaches provided similar results which revealed the existence of a chaotic and fractal dynamics involving the initial conditions and the post-collisional properties of the solitons, which were verified by the analysis of the correlations between the input and output parameters. The fractal patterns are constituted by regularity windows that are positioned accordingly to a well defined rule, which was obtained via a linearization model that was found to be very similar in both approaches (i.e., the windows arrangement was well described by the variational model). In such windows the solitons collision dynamic turns out to be not chaotic (regular collision), it becomes predictable and very well defined, hence the width of these windows provides the conditions in which the control of the interaction is possible. Besides, by analyzing the dynamics of the variational parameters of the reduced model and also the dynamics of the most relevant physical quantities in the exact approach via PDEs (namely the total kinetic and potential energies), we attested that these windows arise due to a resonant mechanism of energy exchange between translational and vibrational soliton modes. By studying the linear stability of the solitary waves, we proved that the vibrational modes originate from shape oscillations induced by internal modes and also, possibly, by instability modes excited during the collisions. We verified that these oscillations are well defined in all regular collisions. The viability of the variational method in the system studied is due to the suitable description of the vibrational modes by the reduced model, and also the low influence of the emitted nonlinear radiation in the regular collision processes found in the direct simulations.Mostrar mais