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Dissertations / Theses on the topic 'Schrödinger, Equation de'

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Published: 4 June 2021
Last updated: 26 October 2024

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1

Di, Cosmo Jonathan. "Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209863.

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The nonlinear Schrödinger equation appears in different fields of physics, for example in the theory of Bose-Einstein condensates or in wave propagation models. From a mathematical point of view, the study of this equation is interesting and delicate, notably because it can have a very rich set of solutions with various behaviours.<p><p>In this thesis, we have been interested in standing waves, which satisfy an elliptic partial differential equation. When this equation is seen as a singularly perturbed problem, its solutions concentrate, in the sense that they converge uniformly to zero outsid
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2

Mugassabi, Souad. "Schrödinger equation with periodic potentials." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/4895.

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The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are presented. The solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that the energy is slightly greater than the maximum value of the potential
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3

Zhang, Deng [Verfasser]. "Stochastic nonlinear Schrödinger equation / Deng Zhang." Bielefeld : Universitätsbibliothek Bielefeld, 2014. http://d-nb.info/1048210359/34.

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4

Banica, Manuela Valeria. "Equation de Schrödinger en milieu inhomogène." Paris 11, 2003. http://www.theses.fr/2003PA112190.

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Cette thèse concerne l'étude de l'équation de Schrödinger et l'impact de l'inhomogénéité du milieu sur les propriétés qualitatives des solutions: propriétés dispersives et existence locale pour l'équation non-linéaire à coefficients variables, phénomènes d'instabilité sur une variété compacte, explosion en temps fini pour le problème de Dirichlet sur un domaine. Dans la première partie on montre la dispersion et les inégalités de Strichartz globales pour l'équation en une dimension, à coefficients fonctions en escalier. On montre aussi que l'inégalité de dispersion n'est plus vraie pour certai
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5

Kazemi, Parimah. "Compact Operators and the Schrödinger Equation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5453/.

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In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on Rn. The paper finishes with a discussion of examples of Schrödinger equations and the solutions.
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Middlemas, Erin. "Soliton Solutions of the Nonlinear Schrödinger Equation." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/honors/66.

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The nonlinear Schrödinger equation is a classical field equation that describes weakly nonlinear wave-packets in one-dimensional physical systems. It is in a class of nonlinear partial differential equations that pertain to several physical and biological systems. In this project we apply a pseudo-spectral solution-estimation method to a modified version of the nonlinear Schrödinger equation as a means of searching for solutions that are solitons, where a soliton is a self-reinforcing solitary wave that maintains its shape over time. The pseudo-spectral method estimates solutions by utilizing
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7

Bader, Philipp Karl-Heinz. "Geometric Integrators for Schrödinger Equations." Doctoral thesis, Universitat Politècnica de València, 2014. http://hdl.handle.net/10251/38716.

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The celebrated Schrödinger equation is the key to understanding the dynamics of quantum mechanical particles and comes in a variety of forms. Its numerical solution poses numerous challenges, some of which are addressed in this work. Arguably the most important problem in quantum mechanics is the so-called harmonic oscillator due to its good approximation properties for trapping potentials. In Chapter 2, an algebraic correspondence-technique is introduced and applied to construct efficient splitting algorithms, based solely on fast Fourier transforms, which solve quadratic potentials in
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8

Vladimir, Lončar. "Hybrid parallel algorithms for solving nonlinear Schrödinger equation." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2017. https://www.cris.uns.ac.rs/record.jsf?recordId=104931&source=NDLTD&language=en.

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Numerical methods and algorithms for solving of partial differential equations, especially parallel algorithms, are an important research topic, given the very broad applicability range in all areas of science. Rapid advances of computer technology open up new possibilities for development of faster algorithms and numerical simulations of higher resolution. This is achieved through paralleliza-tion at different levels that&nbsp; practically all current computers support.In this thesis we develop parallel algorithms for solving one kind of partial differential equations known as nonlinear Schr&
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9

Win, Yin Yin Su. "Unconditional uniqueness of the derivative nonlinear Schrödinger equation." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124386.

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10

Moyano, Garcia Iván. "Controllability of of some kinetic equations, of parabolic degenerated equations and of the Schrödinger equation via domain transformation." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX062/document.

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Ce mémoire présente les travaux réalisés au cours de ma thèse dans le but d'étudier la contrôlabilité de quelques équations aux dérivées partielles. La première partie de cette thèse est consacrée à l'étude de la contrôlabilité de quelques équations cinétiques en différents régimes. Dans un régime collisionnel, nous étudions la contrôlabilité de l'équation de Kolmogorov, un modèle de type Fokker-Planck cinétique, posée dans l'espace de phases $R^d times R^d$. Nous obtenons la contrôlabilité à zéro de cette équation grâce à l'utilisation d'une inégalité spectrale associée à l'opérateur Laplacie
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11

Yasuda, Koji. "Uniqueness of the solution of the contracted Schrödinger equation." American Physical Society, 2002. http://hdl.handle.net/2237/8740.

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12

Nissen, Anna. "Absorbing boundary techniques for the time-dependent Schrödinger equation." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-113087.

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Chemical dissociation processes are important in quantum dynamics. Such processes can be investigated theoretically and numerically through the time-dependent Schrödinger equation, which gives a quantum mechanical description of molecular dynamics. This thesis discusses the numerical simulation of chemical reactions involving dissociation. In particular, an accurate boundary treatment in terms of artificial, absorbing boundaries of the computational domain is considered. The approach taken here is based on the perfectly matched layer technique in a finite difference framework. The errors intro
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13

Bondila, Mariana Mihaela. "Numerical study of the parametrically driven damped nonlinear Schrödinger equation." Master's thesis, University of Cape Town, 1995. http://hdl.handle.net/11427/18240.

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14

Sepùlveda, Salas Paulina Ester. "Spacetime Numerical Techniques for the Wave and Schrödinger Equations." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4206.

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The most common tool for solving spacetime problems using finite elements is based on semidiscretization: discretizing in space by a finite element method and then advancing in time by a numerical scheme. Contrary to this standard procedure, in this dissertation we consider formulations where time is another coordinate of the domain. Therefore, spacetime problems can be studied as boundary value problems, where initial conditions are considered as part of the spacetime boundary conditions. When seeking solutions to these problems, it is natural to ask what are the correct spaces of functions t
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15

Xie, Jian. "On the long time behavior of solutions of Schrödinger's equation." Paris 6, 2011. http://www.theses.fr/2011PA066191.

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Ce mémoire est consacré à l'étude du comportement en temps grand des solutions de l'équation de Schrödinger, linéaire et non-linéaire, posée sur l'espace entier. La première partie est consacrée à l'étude du taux de décroissance temporelle des normes $$L^p$$ des solutions. On montre notamment qu'il existe des solutions régulières qui ne possèdent pas de taux de décroissance défini. La seconde partie est consacrée à l'étude de l'ensemble des points-limites dans les espaces $$L^p$$ des solutions, après un changement d'échelle ad-hoc. On montre qu'il existe des solutions régulières pour lesquels
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16

Teloni, Daniele. "Semiclassical analysis of systems of Schrödinger equations." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19239/.

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The scalar Schrödinger equation models the probability density distribution for a particle to be found in a point x given a certain potential V(x) forming a well with respect to a fixed energy level E_0. Formally two real inversion points a,b exist such that V(a)=V(b)=E_0, V(x)<0 in (a,b) and V(x)>0 for x<a or x>b. Following the work made by D.Yafaev and performing a WKB approximation we obtain solutions defined on specific intervals. The aim of the first part of the thesis is to find a condition on E, which belongs to a neighbourhood of E_0, such that it is an eigenvalue of the Schrödinger op
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17

Riera, Pau. "Conservative high order collocation methods for nonlinear Schrödinger equations." Thesis, Stockholms universitet, Fysikum, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-194703.

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In this thesis, we investigate the numerical solution of time-dependent nonlinear Schrödinger equations (more specifically, the Gross-Pitaevskii equation) that appear in the modeling of Bose-Einstein condensates. Since the model is known to conserve important physical invariants, such as mass and energy of the condensate, our goal is to study the importance of reproducing the conservation on the discrete level. The reliability of conservative, compared to non-conservative, methods shall be studied through high order collocation methods for the time discretization and finite element-based space
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18

Caudrelier, Vincent. "Equation de Schrödinger non-linéaire et impuretés dans les systèmes intégrables." Phd thesis, Chambéry, 2005. http://tel.archives-ouvertes.fr/tel-00009612.

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Cette thèse s'inscrit dans le domaine de physique théorique appelé systèmes intégrables, qui mêle fructueusement physique et mathématiques et se caractérise par la possibilité d'obtenir des résultats exacts (i.e. non perturbatifs) guidant les prédictions physiques qui en découlent. <br />Dans ce contexte, l'équation de Schrödinger non-linéaire (à 1+1 dimensions) est un système privilégié. On la retrouve comme modèle de phénomènes variés tant classiques (optique non-linéaire, mécanique des fluides...) que quantiques (gaz ultra-froids, condensation de Bose-Einstein...). En outre, elle a contribu
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19

Nazaikinskii, Vladimir, and Boris Sternin. "Some problems of control of semiclassical states for the Schrödinger equation." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2613/.

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Contents: Introduction Controlled Quantum Systems The Asymptotic Controllability Problem The Stabilization Problem Unitarily Nonlinear Equations The Quantum Problem The Stabilization Problem for the Schrödinger Equation with a Unitarily Non-linear Control
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20

Gosson, Maurice A. de. "Extended Weyl calculus and application to the phase-space Schrödinger equation." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2987/.

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We show that the Schr¨odinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extendedWeyl calculus obtained by letting the Heisenberg group act on functions (or half-densities) defined on phase space. This allows us, in passing, to solve rigorously the TF equation for all quadratic Hamiltonians.
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21

Roger, Thomas, Calum Maitland, Kali Wilson, et al. "Optical analogues of the Newton–Schrödinger equation and boson star evolution." NATURE PUBLISHING GROUP, 2016. http://hdl.handle.net/10150/622111.

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Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium
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22

Olivier, Carel Petrus. "The direct scattering study of the parametrically driven nonlinear Schrödinger equation." Doctoral thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/4917.

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23

Warren, Oliver H. "A study of finite gap solutions to the nonlinear Schrödinger equation." Thesis, Imperial College London, 2007. http://hdl.handle.net/10044/1/1255.

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The vector nonlinear Schrödinger equation is an envelope equation which models the propagation of ultra-short light pulses and continuous-wave beams along optical fibres. Previous work has focused almost entirely on soliton solutions to the equation using a Lax representation originally developed by Manakov. We prove recursion formulae for the family of higher-order nonlinear Schrödinger equations, along with its associated Lax hierarchy, before investigating finite gap solutions using an algebrogeometric approach which introduces Baker-Akhiezer functions defined upon the Riemann surface of th
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24

Chiu, Hok-shun, and 趙鶴淳. "Stability and interaction of waves in coupled nonlinear Schrödinger type systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43224258.

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25

Yip, Lai-pan, and 葉禮彬. "Nonlinear and localized modes in hydrodynamics and vortex dynamics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39316919.

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26

Tsang, Cheng-hou Alan, and 曾正豪. "Dynamics of waves and patterns of the complex Ginburg Landau and soliton management models: localized gain andeffects of inhomogeneity." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46975433.

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27

Carvalho, Fábio Henrique de. "O grupo de Schrödinger em espaços de Zhidkov." Universidade Federal de Alagoas, 2010. http://repositorio.ufal.br/handle/riufal/1045.

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This work is dedicated to the local and global well-possednes study of Cauchy s Problem associated to the nonlinear Schrödinger equation, to the initial data nonzero at infinity.<br>Conselho Nacional de Desenvolvimento Científico e Tecnológico<br>Este trabalho é dedicado ao estudo da boa colocação local e global do Problema de Cauchy associado à equação não linear de Schrödinger, com dado inicial não nulo no infinito.
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28

Mouzaoui, Lounès. "Régimes asymptotiques pour l'équation de Schrödinger non linéaire non locale." Thesis, Montpellier 2, 2013. http://www.theses.fr/2013MON20241/document.

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Cette thèse est consacrée à l'étude de quelques régimes asymptotiques de l'équation de Schrödinger semi-classique, en présence d'une non-linéarité non-locale de type Hartree. Elle comporte 3 parties, sous forme de 4 chapitres et une annexe. L'objet de la première partie, constituée du premier et deuxième chapitre, est l'étude du comportement asymptotique du modèle précédent pour un noyau singulier autour de l'origine, pour une condition initiale asymptotiquement de type WKB, en régime faiblement non-linéaire. Dans le premier chapitre nous montrons que sous certaines conditions de régularité su
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29

Christodoulides, Yiannis Takis. "Spectral theory of Herglotz functions and their compositions, and the Schrödinger equation." Thesis, University of Hull, 2001. http://hydra.hull.ac.uk/resources/hull:5406.

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In this thesis we generalize the theory of value distribution associated to a Herglotz function. Compositions of Herglotz functions are studied, and some results regarding the integral representation of a composed Herglotz function are obtained. Properties of spectral measures corresponding to Herglotz functions are derived, and an application to the Schrödinger equation is given.
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30

Viklund, Lina, Louise Augustsson, and Jonas Melander. "Numerical approaches to solving the time-dependent Schrödinger equation with different potentials." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-295932.

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This project is an immersive study in numerical methods, focusing on quantum molecular dynamics and methods for solving the time-dependent Schrödinger equation. First the Schrödinger equation was solved with finite differences and a basic propagator in time, and it was then concluded that this method is far too slow and compuationally heavy for its use to be justified for this type of problem. Instead pseudo-spectral methods with split-operators were implemented, and this proved to be a far more favourable method for solving, both in regards to time and memory requirements. Further, the pseudo
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31

Fathe, Jalali Atabak, and Hugo Åkesson. "Comparing Three Numerical Methods For Solving The 1D Time Dependent Schrödinger Equation." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297532.

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The purpose of this thesis is to implement three numerical methods for solving and examining the time-dependent Schrödinger equation (TDSE) of the analytically solved quantum harmonic oscillator (QHO) and the, to our knowledge, analytically unsolved double well potential (DW), and to compare the numerical solutions. These methods are the Crank-Nicolson method and two split operator methods of different orders. For the QHO, the exact solution is used to determine the errors of the methods, while other methods for examining the DW had to be used (due to the lack of exact solutions). The solution
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32

Liu, Jiaqi. "Global Well-posedness for the Derivative Nonlinear Schrödinger Equation Through Inverse Scattering." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/50.

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We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.
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33

Masaki, Satoshi. "Asymptotic expansion of solutions to the nonlinear Schrödinger equation with power nonlinearity." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124383.

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34

Yang, Bole. "Algebraic Aspects of the Dispersionless Limit of the Discrete Nonlinear Schrödinger Equation." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/297064.

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We study the DNLS and its dispersionless limit based on a family of matrices, named after Cantero, Moral, and Velazquez (CMV). The work is an analog to that of the Toda lattice and dispersionless Toda. We rigorously introduce the constants of motion and matrix symbols of the dispersionless limit of the DNLS. The thesis is an algebraic preparation for some potential geometry setup in the continuum sense as the next step.
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Nathanson, Ekaterina Sergeyevna. "Path integration with non-positive distributions and applications to the Schrödinger equation." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1370.

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In 1948, Richard Feynman published the first paper on his new approach to non-relativistic quantum mechanics. Before Feynman's work there were two mathematical formulations of quantum mechanics. Schrödinger's formulation was based on PDE (the Schrödinger equation) and states representation by wave functions, so it was in the framework of analysis and differential equations. The other formulation was Heisenberg's matrix algebra. Initially, they were thought to be competing. The proponents of one claimed that the other was “ wrong. ” Within a couple of years, John von Neumann had proved that the
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36

Kierkels, Arthur H. M. [Verfasser]. "On a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation / Arthur H. M. Kierkels." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1124540202/34.

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37

Mohamad, Haidar. "Sur l'équation de Gross-Pitaevskii uni-dimensionnelle et quelques généralisations du flot par courbure binormale." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066176.

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Ce travail est une contribution à l'étude des équations de Schrödinger non-linéaires (NLS) en dimension un d'espace. De telles équations interviennent notamment comme modèles dans plusieurs domaines de la physique mathématique, tels l'optique non-linéaire, la superfluidité, la supraconductivité et la condensation de Bose-Einstein.Cette thèse contient trois thèmes connexes inclus dans les chapitres 2, 3 et 4. Dans la première partie (chapitre 2), on s'intéresse à la construction des solutions en multi-solitons de l'équation de Gross-Pitaevskii (NLS défocalisante avec non-linéarité cubique), com
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38

Chang, Paul C. "Modulational stability of oscillatory pulse solutions of the parametrically-forced nonlinear Schrödinger equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ61540.pdf.

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Borghese, Michael, and Michael Borghese. "A Proof of the Soliton Resolution Conjecture for the Focusing Nonlinear Schrödinger Equation." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624578.

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We give a proof of the long-time asymptotic behavior of the focusing nonlinear Schrödinger equation for generic initial condition in which we have simple discrete spectral data and an absence of spectral singularities. The proof relies upon the theory of Riemann-Hilbert problems and the ∂ ̄ method for nonlinear steepest descent. To leading order, the solution will appear as a multi-soliton solution as t → ∞.
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Marshall, William. "Towards quantum superpositions of a mirror." Thesis, University of Oxford, 2004. http://ora.ox.ac.uk/objects/uuid:54b68fad-5adb-4a32-af41-064dda4b5f77.

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In principle Quantum Mechanics allows the creation of macroscopic mass superposition states - so called "Schrödinger Cat States". This has not been confirmed experimentally largely due to the difficulty of isolating such states from environmental decoherence. It is of interest to create massive superpositions both in order to test Quantum Mechanics and to shed light on the elusive 'measurement problem'. This thesis presents the theoretical analysis of, and the initial experimental steps towards, an ambitious proposal to test the superposition principle of Quantum Mechanics at the 10<sup>-12</s
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Wanelik, Kazimierz. "Some aspects of adiabatic evolution." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670282.

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42

Mejri, Youssef. "Problèmes inverses pour l’équation de Schrödinger." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0506/document.

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Les travaux de recherche présentés dans cette thèse sont consacrés à l’étude de la stabilité dans divers problèmes inverses associés à l’équation de Schrödinger magnétique. Dans la première partie, on s’intéresse à un problème inverse concernant l’équation de Schrödinger autonome posée dans un domaine cylindrique non borné, avec potentiel magnétique périodique. On démontre à l’aide d’une construction de solutions particulières, dites solutions de type "optique géométrique", que le champ magnétique induit par le potentiel périodique est déterminé de façon stable à partir une infinité d’observat
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Arroyo, Meza Luis Enrique [UNESP]. "Equação de Schrödinger não linear com coeficientes modulados." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/127728.

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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)<br>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 transformaçõe
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Arroyo, Meza Luis Enrique. "Equação de Schrödinger não linear com coeficientes modulados /." Guaratinguetá, 2015. http://hdl.handle.net/11449/127728.

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Orientador: Marcelo Batista Hott<br>Coorientador: Alvaro de Souza Dutra<br>Banca: Denis Dalmazi<br>Banca: Roberto André Kraenkei<br>Banca: Othon Cabo Winter<br>Wesley Bueno Cardoso<br>Resumo: 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 Schro
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45

Johansson, Karoline. "A counterexample concerning nontangential convergence for the solution to the time-dependent Schrödinger equation." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1082.

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<p>Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|
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46

Coles, Matthew Preston. "Behaviour of solutions to the nonlinear Schrödinger equation in the presence of a resonance." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/62655.

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The present thesis is split in two parts. The first deals with the focusing Nonlinear Schrödinger Equation in one dimension with pure-power nonlinearity near cubic. We consider the spectrum of the linearized operator about the soliton solution. When the nonlinearity is exactly cubic, the linearized operator has resonances at the edges of the essential spectrum. We establish the degenerate bifurcation of these resonances to eigenvalues as the nonlinearity deviates from cubic. The leading-order expression for these eigenvalues is consistent with previous numerical computations. The second cons
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47

Kerdelhué, Philippe. "Equation de Schrödinger magnétique périodique avec symétries triangulaires et hexagonales : structure hiérarchique du spectre." Paris 11, 1991. http://www.theses.fr/1991PA112051.

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On etudie l'equation de schrodinger en dimension deux, en presence d'un champ magnetique et d'un potentiel periodique et possedant une symetrie de rotation d'ordre six. On traite les cas dits triangulaires et hexagonaux qui sont ceux ou le potentiel atteint son minimum une ou deux fois par cellule de periodicite. Sous l'hypothese que la constante de planck est assez petite, on montre que la partie inferieure du spectre de ces operateurs est le spectre d'operateurs pseudo-differentiels, quantifies avec une nouvelle constante de planck, et dont on peut approcher les symboles. Si cette nouvelle c
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48

ABDELHAKIM, MOUHAMED Ahmed Abdelsattar. "On the space - time integrability properties of the solution of the inhomogeneous Schrödinger equation." Doctoral thesis, Università degli studi di Ferrara, 2013. http://hdl.handle.net/11392/2388925.

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49

Thomann, Laurent. "Instabilité des équations de Schrödinger." Phd thesis, Université Paris Sud - Paris XI, 2007. http://tel.archives-ouvertes.fr/tel-00265284.

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Dans cette thèse on s'est intéressé à différents phénomènes d'instabilités pour des équations de Schrödinger non-linéaires.<br /> Dans la première partie on met en évidence un mécanisme de décohérence de phase pour l'équation (semi-classique) de Gross-Pitaevski en dimension 3. Ce phénomène géométrique est dû à la présence du potentiel harmonique, qui permet de construire -via une méthode de minimisation- des solutions stationnaires se concentrant sur des cercles de R^{3}.<br /> Dans la deuxième partie, on obtient un résultat d'instabilité géométrique pour NLS cubique posée sur une surface riem
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50

Gonzaga, Anderson dos Santos [UNESP]. "Resultados de existência de soluções para problemas elípticos assintoticamente lineares." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152494.

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