Submitted by Simone Souza (simonecgsouza@hotmail.com) on 2018-04-20T15:11:04Z No. of bitstreams: 1 DISS_2014_Leonides da Rocha Mota.pdf: 1237393 bytes, checksum: 143ba9211bb27429e5a7a12c52f58839 (MD5) / Approved for entry into archive by Jordan (jordanbiblio@gmail.com) on 2018-05-14T16:48:32Z (GMT) No. of bitstreams: 1 DISS_2014_Leonides da Rocha Mota.pdf: 1237393 bytes, checksum: 143ba9211bb27429e5a7a12c52f58839 (MD5) / Made available in DSpace on 2018-05-14T16:48:32Z (GMT). No. of bitstreams: 1 DISS_2014_Leonides da Rocha Mota.pdf: 1237393 bytes, checksum: 143ba9211bb27429e5a7a12c52f58839 (MD5) Previous issue date: 2014-02-07 / CAPES / Neste trabalho, examinamos a integrabilidade do modelo generalizado de sine-Gordon (GsG), no contexto do teste de Painlevé para equações diferenciais parciais (EDPs). Mostramos que o modelo (GsG) possui certos submodelos como o modelo duplo sine-Gordon (DsG), Bukhvostov-Lipatov (BL) e os modelos integráveis sine-Gordon. O modelo BL possui algumas direções integráveis no espaço dos campos. Classi camos as massas das soluções tipo sólitons (kinks) do modelo (GsG) através dos pesos máximos da álgebra de Lie sl(3), e mostramos que essas massas pertencem a determinados multipletos neste esquema de representação. Abordamos o modelo integrável NLS defocusing e estudamos a colisão de dois sólitons dark, em particular estudamos a mudança de fase após a sua colisão. / In this work the integrability of the generalized sine-Gordon model (GsG) is examined in the context of the Painlevé test for partial di erential equations (PDEs). We show that the (GsG) model possesses certain submodels such as the double sine-Gordon (DsG), Bukhvostov-Lipatov (BL) and the integrable sine-Gordon models. The BL model possesses some integrable directions in the eld space. Moreover, we classify the kink type solutions of the (GsG) model through the highest weight representations of the underlying sl(3) Lie algebra, and we show that these masses belong to certain multiplets in that representation scheme. We discussed the integrable defocusing NLS model and study the collision of two dark solitons, in particular we study the phase shift after their collision.