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O teste de Painlevé e a integrabilidade do modelo generalizado de sine-GordonMota, Leonides da Rocha 07 February 2014 (has links)
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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.
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