Made available in DSpace on 2015-09-17T15:25:12Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-20. Added 1 bitstream(s) on 2015-09-17T15:49:08Z : No. of bitstreams: 1 000846817.pdf: 2163733 bytes, checksum: ff2516a4b76821b3ebeb84675776dd6d (MD5) / Nesta tese lidamos com a equação de Schroedinger não linear com coeficientes modulados em diferentes contextos. Esta equação diferencial não linear é amplamente usada para descrever a propagação de pulsos de luz através de uma fibra óptica ou para modelar a dinâmica de um condensado de Bose-Einstein. Primeiro, aplicamos as transformações canônicas de ponto para resolver algumas classes de equação de Schroedinger não linear com coeficientes modulados ou seja, aqueles que possuem não linearidades cúbica e quântica (dependentes do espaço e tempo) específicas. O método aplicado aqui nos permite encontrar soluções tipo sólitons localizados (no espaço) para a equação de Schroedinger não linear com coeficientes modulados, que não foram apresentados antes. No contexto de condensados de Bose-Einstein, nós generalizamos o potencial externo o qual armadilha o sistema, e os termos de não linearidade da equação diferencial. Em seguida, aplicamos as transformações canônicas de ponto para resolver algumas classes de duas equações de Schroedinger não lineares acopladas com coeficientes modula-dos isto é, não linearidades cúbica e quântica - dependentes do espaço e tempo - específicas. O método aplicado aqui nos permite encontrar uma classe de soluções de sólitons tipo vetoriais localizados (no espaço) das duas equações de Schroedinger não linear acopladas. Os sólitons vetoriais encontrados aqui podem ser aplicados a estudos teóricos de condensados de Bose-Einstein de átomos com dois estados internos diferentes ou á propagação de pulsos de luz através de fibras ópticas focalizadoras ou desfocalizadoras. Finalmente, usando transformações canônicas de ponto obtemos soluções exatas localizadas (no espaço) da equação de Schroedinger não linear com não linearidades cúbica e quântica moduladas no espaço e tempo ...(Resumo completo, clicar acesso eletrônico abaixo) / In this thesis we deal with the nonlinear Schrödinger equation with modulated coefficients in different contexts. This nonlinear differential equation is widely used to describe light pulses propagating through an optical fiber or to model the dynamics of a Bose-Einstein condensate. First, we apply point canonical transformations to solve some classes of nonlinear Schrödinger equation with modulated coefficients namely, those which possess specific cubic and quantic (time- and space-dependent) nonlinearities. The method applied here allows us to find wide localized (in space) soliton solutions to the nonlinear Schrödinger equation, which were not presented before. In the context of Bose-Einstein condensates, we also generalize the external potential which traps the system and the nonlinearities terms. Then, we apply point canonical transformations to solve some classes of two coupled nonlinear Schrödinger equations with modulated coefficients namely, specific cubic and quantic - time and space dependent - nonlinearities. The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of two coupled nonlinear Schrödinger equations. The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. Finally, we use point canonical transformations to obtain localized (in space) exact solutions of the nonlinear Schrödinger equation with cubic and quantic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) term. We obtain a class of wide localized exact solutions of nonlinear Schrödinger equation in the presence of a number of non-Hermitian ... (Complete abstract click electronic access below)

Orientadores: Marcia Assumpção Guimarães Scialom, Felipe Linares / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-10T05:23:45Z (GMT). No. of bitstreams: 1 Braganca_LucianaMariaMendonca_D.pdf: 688598 bytes, checksum: af92575e77efea7c1bdd4a624c7d70dc (MD5) Previous issue date: 2007 / Resumo: Neste trabalho estudamos o problema de Cauchy associado a um sistema de Equações do tipo Schrodinger não linear de terceira ordem. Obtemos resultados de boa colocação local para o problema, com dado inicial nos espaços de Sobolev Hs(R) x Hs(R), s '> ou =' 1/4 e no caso períodico em Hs(T)xHs(T), s '> ou =' 1/2. No caso particular'sigma' 'alfa' = 'sigma' 'beta' = 'sigma''mu' = 1 obtemos resultados de boa colocação global em Hs(R) x Hs(R), 3/5 < s '> ou = 1 e H1(T) x H1(T). Mostramos também um resultado de má colocação para o problema com dado inicial em Hs(R) x Hs(R), -1/2 < s < 1/4 / Abstract: In this work we study the Cauchy problem associated to a system of coupled third-order nonlinear Schrodinger equation. We establish local well-posedness results for the problem with data in Sobolev spaces Hs(R) x Hs(R), s '> or =' 1/4 and in the periodic case Hs(T)xHs(T), s '> or =' 1/2. In the particular case ... Note: The complete abstract is available with the full electronic digital thesis or dissertations / Doutorado / Doutor em Matemática

Orientadores: João Marcos Bezerra do O, Orlando Francisco Lopes / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-09T00:03:49Z (GMT). No. of bitstreams: 1 Severo_UberlandioBatista_D.pdf: 985878 bytes, checksum: 9d6e8a161a83e2812687d6ed4364bda1 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho, estudamos questões relacionadas à existência, multiplicidade e comportamento de concentração de soluções do tipo onda estacionária, para uma classe de equações de Schrödinger quase-lineares, as quais modelam fenômenos físicos, por exemplo, na F³sica de Plasmas. Na obtenção de nossos resultados, usamos métodos variacionais, tais como, teoremas do tipo mini-max, bem como, teoria de regularidade de equações elípticas de segunda ordem / Abstract: In this work, we study questions related to existence, multiplicity and concentration behavior of standing waves, for a class of quasilinear Schrödinger equations, arising, for example, in Plasma Physics. To obtain our results, we use variational methods, such as, minimax theorems and also regularity theory of elliptic equations of second order / Doutorado / Analise / Doutor em Matemática

Orientadores: João Marcos Bezerra do O, Djairo Guedes de Figueiredo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-15T15:20:37Z (GMT). No. of bitstreams: 1 Moraes_ElisandradeFatimaGlossde_D.pdf: 1261630 bytes, checksum: 516f800553b6eff1f3462fe4be134e8a (MD5) Previous issue date: 2010 / Resumo: Neste trabalho, estudamos questões relacionadas com existência e concentração de soluções positivas para algumas classes de problemas elípticos quase-lineares. Na obtenção de nossos resultados usamos um método variacional que permite estudar soluções do tipo "singlepeak" e "multiple-peak" para uma classe bem geral de não linearidades que não satisfazem necessariamente a condição clássica de Ambrosetti-Rabinowitz bem como nenhuma hipótese de monotonicidade. Problemas deste tipo aparecem em vários modelos da física e biologia, onde a presença de pequenos parâmetros de difusão ocorre naturalmente. Na Física de Plasmas, por exemplo, surgem no estudo de ondas estacionárias para certas classes de problemas envolvendo equações de Schrödinger quase-lineares / Abstract: In this work we study questions related with existence and concentration of positive solutions for some classes of quasilinear elliptic problems. To obtain our results we use a variational method that allows us to study solutions of the "single-peak" and "multiple-peak" type for a more general class of nonlinearities which do not satisfy necessarily the Ambrosetti-Rabinowitz condition and monotonicity hypothesis. Problems of this type appear in several models of physics and biology where the presence of small parameters of difusion occurs naturally. In plasma physics for example, they arise in the study of stationary waves for certain classes of quasilinear Schrödinger equations / Doutorado / Analise / Doutor em Matemática

Orientador: Jaime Angulo Pava / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T02:39:00Z (GMT). No. of bitstreams: 1 Moura_RogerPeresde_D.pdf: 2234766 bytes, checksum: 9c36c9be07d4a5910fabe79366fd1e13 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho estabelecemos algumas propriedades da equação de Schr6dinger nãolinear não-local (NLSNL), em especial as relacionadas ao problema de Cauchy. Primeiramente fizemos um capítulo preliminar de notações e teoria básica utilizada no esta- belecimento dos resultados; essa parte também visa facilitar a leitura do trabalho. Em seguida apresentamos o principal resultado: boa colocação local para o problema de valor inicial (problema de Cauchy) associado à equação NLSNL para dados iniciais pequenos nos espaços de Sobolev reais usuais de ordem maior que três meios; o método permite estabelecer que a aplicação dado inicial-solução é suave. No capítulo seguinte provamos o mesmo resultado para a equação de Schr6dinger não-linear não-Iocal intermediária (INLSNL), a qual é mais geral que a outra. Depois estabelecemos boa colocação para a equação NLSNL em espaços de Sobolev com peso. Em outro capítulo apresentamos um resultado de má colocação: estabelecemos que não se pode obter boa colocação local, em espaços de Sobolev de índice negativo, para o PVI associado à equação NLSNL por meio de método iterativo de Picard; como conseqüência, a aplicação dado-solução não é suave nesses espaços. Provamos também, fazendo uso de uma identidade de Pohozaev, a não existência de soluções standing waves para a equação NLS não-local. Finalizamos com um capítulo onde exibimos alguns problemas interessantes relacionados principalmente à equação NLSNL e algumas possíveis dificuldades a serem enfrentadas em uma eventual tentativa de solucioná-Ios / Abstract: ln this work we establish some properties of the nonlocal nonlinear Schrodinger equation (NLSNL). First of alI, we present a preliminary chapter with notations and basic theory used to establish our results; that part also seeks to facilitate the reading of this work. Soon afterwards comes the main result: local welI-posedness for the initial value problem (the Cauchy problem or lVP) for the NLSNL equation with initial data in real Sobolev spaces of index larger than three and a half; the method of proof alIows to es- tablish that the data-solution map is smooth. ln the folIowing chapter we proved that previous result for the intermediate nonlocal nonlinear Schrüdinger (lNLSNL), which is more general than the NLSNL equation. After that we establish local welI-posedness for the NLSNL equation in weighted Sobolev spaces. ln another chapter the ill-posedness issue is discussed: we established that one cannot obtain local welI-posedness, in Sobolev spaces of negative index, for the lVP associated to NLSNL equation through a iterative Picard method; as a consequence, the data-solution map is not smooth in those spaces. We also proved, making use of a Pohozaev's identity, the no-existence of standing waves solutions for the NLSNL equation. We concluded with a chapter where we exhibited some interesting problems mainly related to the NLSNL equation and possible difficulties to be faced in an eventual attempt of solving them / Doutorado / Matematica / Doutor em Matemática

No description available.

The fully quantum mechanical 'direct-potential-fit' (DPF) method has become increasingly widely used in the reduction of diatomic spectra. The central problem of this method is the representation of the potential energy and Born-Oppenheimer breakdown (BOB) correction functions. There are a number of problems associated with the existing method and potential forms. This thesis delineates these problems and finds solutions to some of them. In particular, it is shown that use of a different expansion variable and a new treatment of some of the expansions resolves most of the problems. These techniques have been successfully tested on the ground electronic states of the coinage metal hydrides and the Rb2 molecule. To address the problem of representing 'barrier' potential curves, a flexible new functional form, the 'double-exponential long-range' (DELR) potential function, is introduced and applied to the B barrier state of Li2. In addition, the Lambda-doubling level splitting which occurs for singlet Pi electronic states has been taken into account by extending the effective Schrodinger equation. The computer program DSPotFit developed in our laboratory for performing DPF analyses has been extended to incorporate the ability to fit the analytical potential energy functions to tunneling predissociation line widths for quasibound levels. Finally, an attempt is made to investigate whether there exists a hump in the ground state rotationless potential curve of beryllium hydride.

The fully quantum mechanical 'direct-potential-fit' (DPF) method has become increasingly widely used in the reduction of diatomic spectra. The central problem of this method is the representation of the potential energy and Born-Oppenheimer breakdown (BOB) correction functions. There are a number of problems associated with the existing method and potential forms. This thesis delineates these problems and finds solutions to some of them. In particular, it is shown that use of a different expansion variable and a new treatment of some of the expansions resolves most of the problems. These techniques have been successfully tested on the ground electronic states of the coinage metal hydrides and the Rb2 molecule. To address the problem of representing 'barrier' potential curves, a flexible new functional form, the 'double-exponential long-range' (DELR) potential function, is introduced and applied to the B barrier state of Li2. In addition, the Lambda-doubling level splitting which occurs for singlet Pi electronic states has been taken into account by extending the effective Schrodinger equation. The computer program DSPotFit developed in our laboratory for performing DPF analyses has been extended to incorporate the ability to fit the analytical potential energy functions to tunneling predissociation line widths for quasibound levels. Finally, an attempt is made to investigate whether there exists a hump in the ground state rotationless potential curve of beryllium hydride.

There has been much work on electron emission. It has lead to the concept of the photon and new electron sources for imaging such as electron microscopes and the rst formulation of holographic reconstructions [1-6]. Analytical derivations are important to gain physical insight into the problem of developing better electron sources. However, to date, such formulations have su ered by a number of approximations that have masked important physics. In this thesis, a new approach is provided that solves the Schrodinger wave equation for photoemission from a single atom tungsten tip barrier or more generally, for photoemission from a Schottky triangular barrier potential, with or without image potential e ects. We describe the system, then introduce the mathematical derivation. We conclude with the applications of the theory.

There has been much work on electron emission. It has lead to the concept of the photon and new electron sources for imaging such as electron microscopes and the rst formulation of holographic reconstructions [1-6]. Analytical derivations are important to gain physical insight into the problem of developing better electron sources. However, to date, such formulations have su ered by a number of approximations that have masked important physics. In this thesis, a new approach is provided that solves the Schrodinger wave equation for photoemission from a single atom tungsten tip barrier or more generally, for photoemission from a Schottky triangular barrier potential, with or without image potential e ects. We describe the system, then introduce the mathematical derivation. We conclude with the applications of the theory.