2022-08-052022-08-052019-02-28SANTOS, Mateus C. P. Redução dimensional para condensados de Bose-Einstein em forma de “tubo” e “anilha plana”. 2019. 54 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/12236The 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.Condensado de Bose-EinsteinEquação de Gross-PitaevskiiRedução dimensionalBose–Einstein condensateGross–Pitaevskii equationDimensional reductionCIENCIAS EXATAS E DA TERRA::FISICA::FISICA GERALDissertação