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Dissertations / Theses on the topic 'Soliton solutions'

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Published: 4 June 2021
Last updated: 25 July 2025

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1

Renger, Walter. "Limits of soliton solutions /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9823316.

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2

Sooman, Craig. "Soliton solutions of noncommutative integrable systems." Thesis, University of Glasgow, 2010. http://theses.gla.ac.uk/1449/.

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This thesis is concerned with solutions of noncommutative integrable systems where the noncommutativity arises through the dependent variables in either the hierarchy or Lax pair generating the equation. Both Chapters 1 and 2 are entirely made up of background material and contain no new material. Furthermore, these chapters are concerned with commutative equations. Chapter 1 outlines some of the basic concepts of integrable systems including historical attempts at finding solutions of the KdV equation, the Lax method and Hirota's direct method for finding multi-soliton solutions of an integra
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3

Reis, Philip Axel. "Soliton solutions to Calogero-Moser systems." Thesis, KTH, Fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-265631.

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4

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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5

Morrison, Alan James. "Soliton solutions of some novel nonlinear evolution equations." Thesis, University of Strathclyde, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248782.

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6

Makhankov, Vladimir, та Granados Máximo Agüero. "Bubbles Soliton Solutions in the φᶝ - Field Theory". Pontificia Universidad Católica del Perú, 2002. http://repositorio.pucp.edu.pe/index/handle/123456789/95741.

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7

Zhou, Yuan. "Lump, complexiton and algebro-geometric solutions to soliton equations." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6988.

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In chapter 2, we study two Kaup-Newell-type matrix spectral problems, derive their soliton hierarchies within the zero curvature formulation, and furnish their bi-Hamiltonian structures by the trace identity to show that they are integrable in the Liouville sense. In chapter 5, we obtain the Riemann theta function representation of solutions for the first hierarchy of generalized Kaup-Newell systems. In chapter 3, using Hirota bilinear forms, we discuss positive quadratic polynomial solutions to generalized bilinear equations, which generate lump or lump-type solutions to nonlinear evolution e
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8

Allami, Mohammed Jabbar Hawas. "Soliton equations in two spatial dimensions and their solutions." Thesis, University of Kent, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.587561.

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This thesis concerns soliton equations in two spatial dimensions. Camassa and Holm derived a model of shallow water wave which continues to attract attention in the light of the remarkable wealth of mathematical and physical properties of its solutions. More recently, Kraenkel and Zenchuk introduced an extension of Camassa and Holm's equation to two spatial dimensions, with three fields, and derived it from a Lax pair. However, finding solutions of this model is more challenging. In order to understand and find solutions of the (2 + l)-dimensional Camassa- Holm (CH) equation, it turns out that
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9

Bury, Rhys Thomas. "Automorphic lie algebras, corresponding integrable systems and their soliton solutions." Thesis, University of Leeds, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.539708.

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10

陶福臻 and Fook-tsun To. "Soliton solutions to gravitational field and Yang-Mills gauge field." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233910.

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11

To, Fook-tsun. "Soliton solutions to gravitational field and Yang-Mills gauge field /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13671728.

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12

Nkeumaleu, Guy-Merlin. "Propagation d'informations le long d'une ligne de transmission non linéaire structurée en super réseau et simulant un neurone myélinisé." Thesis, Bourgogne Franche-Comté, 2019. http://www.theses.fr/2019UBFCK006/document.

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Les systèmes non linéaires sont décrits pour la plupart avec des équations aux dérivées partiellesqui les caractérisent, comme la chaine de pendules couplés, la chaine de protéines comportant des molécules avec liaisons hydrogène, les réseaux atomiques ...etc. Ces modèles comportent le plus souvent des interactions inter particulaires anharmoniques et des potentiels de substrat déformables. En effet, aux conséquences importantes dues à la non linéarité et à la dispersion, ces autres phénomènes comme l’anharmonicité et la déformabilité conduisent à d’autres propriétés de propagation des ondes s
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13

Rubiera, García Diego. "Relativistic lagrangian non-linear field theories supporting non-topological soliton solutions." Doctoral thesis, Universidad de Oviedo, 2008. http://hdl.handle.net/10803/11131.

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En el contexto de la teoría de campos el interés en soluciones extendidas describiendo campos asociados a partículas puntuales data de los años 30, con los intentos de Born e Infeld para construir una electrodinámica no-lineal cuyas soluciones electrostáticas a simetría esférica eliminaran la divergencia de la autoenergía del electrón en Electrodinámica Clásica.En esta tesis realizamos un amplio estudio de una extensa clase de teorías relativistas de campos que contienen soluciones de tipo solitón no-topológico en tres dimensiones espaciales. Específicamente estudiamos campos (multi) escalares
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14

李達明 and Tad-ming Lee. "Isospectral transformations between soliton-solutions of the Korteweg-de Vries equation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B29866261.

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15

Lee, Tad-ming. "Isospectral transformations between soliton-solutions of the Korteweg-de Vries equation /." [Hong Kong : University of Hong Kong], 1994. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1359753X.

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16

Isa, Mukheta Bin. "A study of the soliton solutions of the Boussinesq and other nonlinear evolution equations of fluid mechanics." Thesis, University of Newcastle Upon Tyne, 1988. http://hdl.handle.net/10443/723.

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After introducing the nonlinear evolution equations of interest: the finite depth fluid (FDF), the Kadomtsev-Petviashvili (KP), the Classical and the ordinary Boussinesq equations, formal asymptotic derivations of the KP and the FDF equations are given for the description of surface and interfacial waves. The N-soliton solution of the FDF equation is reconstructed as a finite sum of Wronskian type determinants. This solution is then shown to reduce to the solutions of the KdV and the Benjamin - Ono equations under specific limiting conditions. Interactions between two solitons of the FDF equat
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17

Barran, Sunil Kumar. "Modulation of the harmonic soliton solutions for the defocusing nonlinear Schroedinger equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ40028.pdf.

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18

霍逸遠 and Yat-yuen Eric Fok. "Soliton solutions of nonisospectral variable-coefficient evolution equations via Zakharov-Shabat dressing method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31213078.

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19

Lindgren, Joseph B. "Orbital Stability Results for Soliton Solutions to Nonlinear Schrödinger Equations with External Potentials." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/46.

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For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method. For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.
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20

Fok, Yat-yuen Eric. "Soliton solutions of nonisospectral variable-coefficient evolution equations via Zakharov-Shabat dressing method /." Hong Kong : University of Hong Kong, 1996. http://sunzi.lib.hku.hk/hkuto/record.jsp?B17506177.

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21

Vogel, Thomas. "SOLITON SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS USING VARIATIONAL APPROXIMATIONS AND INVERSE SCATTERING TECHNIQUES." Doctoral diss., University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3506.

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Throughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of variational approximations and inverse scattering transform. Additionally, a new technique for estimating the er
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22

Hårderup, Peder, and William Brorsson. "A Numerical and Analytical Investigation of The sine-Gordon Equation and Its Soliton Solutions." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297564.

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This thesis investigates the nonlinear partial differential equation known as sine-Gordon and its special soliton solutions.Simpler analytical results are derived and more advanced methods and their results are discussed.Further, a finite difference scheme is derived, implemented and compared against a known energy conserving scheme of sine-Gordon in terms of stability, accuracy, convergence and computation time.The complete solvability of the equation enables comparison between numerical solutions and their analytical counterparts.No unified answer to which numerical scheme is best was determ
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23

Waterton, Richard James. "Analysis of the soliton solutions of a 3-level Maxwell-Bloch system with rotational symmetry." Thesis, University of Glasgow, 2004. http://theses.gla.ac.uk/3867/.

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The dynamics of soliton pulses for use in nonlinear optical devices is mathematically modelled by Maxwell-Bloch systems of equations for the interaction of light with a uniform distribution of quantum-mechanical atoms. We study the Reduced Maxwell-Bloch (RMB) equations occurring when an ensemble of rotationally symmetric 3-level atoms is assumed. The model applies for on and off-resonance conditions and is completely integrable using Inverse Scattering theory, since it arises as the compatibility condition of a 3 x 3 AKNS-system. Furthermore this integrability remains valid for all timescales
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24

Ortoleva, Cecilia Maria. "Asymptotic properties of the dynamics near stationary solutions for some nonlinear Schrödinger équations." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00825627.

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The present thesis is devoted to the investigation of certain aspects of the large time behavior of the solutions of two nonlinear Schrödinger equations in dimension three in some suitable perturbative regimes. The first model consist in a Schrödinger equation with a concentrated nonlinearity obtained considering a {point} (or contact) interaction with strength $alpha$, which consists of a singular perturbation of the Laplacian described by a self adjoint operator $H_{alpha}$, and letting the strength $alpha$ depend on the wave function: $ifrac{du}{dt}= H_alpha u$, $alpha=alpha(u)$.It is well-
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25

Wiggins, Benjamin. "Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/751.

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This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons. Through variable transformation and use of the Hirota derivative, these nonlinear partial differential equations can be expressed in bilinear form. We present both Wronskian and Gram determinants which satisfy the equations. N=1,2,3 and higher order solutions are presented graphically; parameter tuning and the resultant behavioral differences are demonstrated and discussed. In addition, we compare the
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26

Caldwell, Trevor. "Nonlinear Wave Equations and Solitary Wave Solutions in Mathematical Physics." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/32.

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In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinear wave equations from which they arise. We focus on a semilinear perturbation of Maxwell's equations and the nonlinear Klein - Gordon equation coupled with Maxwell's equations. Physical ramifications of
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27

ORTOLEVA, CECILIA MARIA. "Asymptotic properties of the dynamics near stationary solutions for some nonlinear schro dinger equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/41846.

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The present thesis is devoted to the investigation of certain aspects of the large time behavior of the solutions of two nonlinear Schrödinger equations in dimension three in some suitable perturbative regimes. The rst model consist in a Schrödinger equation with a concentrated nonlinearity obtained considering a point (or contact) interaction with strength , which consists of a singular perturbation of the Laplacian described by a selfadjoint operator H , and letting the strength depend on the wave function: i du dt = H u, = (u). It is well-known that the elements of the domain
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28

Körner, Stefan [Verfasser]. "Mapping Properties of Bäcklund Transformations and the Asymptotic Stability of Soliton Solutions for the Nonlinear Schrödinger and Modified Korteweg-de-Vries Equation / Stefan Körner." Bonn : Universitäts- und Landesbibliothek Bonn, 2020. http://d-nb.info/1206417579/34.

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29

Haberichter, Mareike Katharina. "Classically spinning and isospinning non-linear σ-model solitons". Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/classically-spinning-and-isospinning-nonlinear-sigmamodel-solitons(59f1d53d-0de7-4938-ad02-85ac57f6003f).html.

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We investigate classically (iso)spinning topological soliton solutions in (2+1)- and (3+1)-dimensional models; more explicitly isospinning lump solutions in (2+1) dimensions, Skyrme solitons in (2+1) and (3+1) dimensions and Hopf soliton solutions in (3 +1) dimensions. For example, such soliton types can be used to describe quasiparticle excitations in ferromagnetic quantum Hall systems, can model spin and isospin states of nuclei and may be candidates to model glueball configurations in QCD.Unlike previous work, we do not impose any spatial symmetries on the isospinning soliton configurations
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30

Pavón, Torres Omar. "Estudio de la dinámica interna del ADN gobernada por la ecuacion no lineal de Schrodinger generalizada." Tesis de doctorado, Universidad Autónoma del Estado de México, 2020. http://hdl.handle.net/20.500.11799/109974.

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La tesis se sustento bajo la categoría de Mención Honorifica<br>el presente trabajo se estudió la dinámica interna de la forma B del ADN interactuando con una proteina mediante la generalización de un modelo aproximado con torsión. Propuesto originalmente por Shozo Takeno y Shigeo Homma, el modelo se basa principalmente en los grados de la libertad de las rotaciones angulares de los pares de bases en un plano normal a ellas. Los posibles modos de deformación de la macromolécula y las energías principales que contribuyen a la conformación y estabilidad del ADN - como lo son la energía de api
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31

ANTONELLI, Riccardo. "Black Objects without a Vacuum." Doctoral thesis, Scuola Normale Superiore, 2020. http://hdl.handle.net/11384/95124.

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We explore the behavior of gravitational solitons in classical theories with pathological vacua. We first focus on non-tachyonic non-supersymmetric string theories and the construction of brane solutions in the corresponding effective theories, which do not admit a maximally-symmetric vacuum. We then turn to metastable vacua and the holographic interpretation of the vacuum bubbles that may be produced therein by quantum tunneling. Finally, we discuss self-similar collapse solutions, with an eye to analogies with the settings considered in the preceding chapters.
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32

Lee, Chun-Te. "Multi-soliton solution of the two-mode KdV equation." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.531973.

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33

Sun, Yue. "Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations." Scholar Commons, 2016. http://scholarcommons.usf.edu/etd/6146.

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In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by Dp-operators with p = 5, which have resonant solutions. We construct resonant solutions by using the linear superposition principle and parameterizations of wave numbers and frequencies. We test different values of p in Maple computations, and generate three classes of generalized bilinear differential equations and their resonant solutions when p = 5.
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34

Correa, Rafael Augusto Couceiro [UNESP]. "Estudo de sistemas não lineares em teoria de campos em baixas dimensões." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/99355.

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Made available in DSpace on 2014-06-11T19:30:11Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-08-20Bitstream added on 2014-06-13T18:59:53Z : No. of bitstreams: 1 correa_rac_me_guara.pdf: 727192 bytes, checksum: e893f54f230b703f5d40233d4e8e1002 (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Neste trabalho, apresentamos uma breve introdução ao estudo dos sólitons. Além disso, introduzimos uma nova classe de configurações oscilantes do tipo lump e do tipo kink. Tais configurações são obtidas de forma analítica e exata, como conseqüência somos capazes de
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35

Erman, Fatih Erdem Recai. "Solitonic solutions and particle localization in higher dimensional spaces/." [s.l.]: [s.n.], 2003. http://library.iyte.edu.tr/tezler/master/fizik/T000278.pdf.

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36

Kazeykina, Anna. "Solitons and large time asymptotics of solutions for the Novikov-Veselov equation." Palaiseau, Ecole polytechnique, 2012. https://pastel.hal.science/docs/00/76/26/62/PDF/these.pdf.

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Ce travail est consacré à l'étude de l'équation de Novikov-Veselov, un analogue ( 2 + 1 )-dimensionnel de l'équation renommée de Korteweg-de Vries, intégrable via la transformée de la diffusion inverse pour l'équation de Schrödinger stationnaire en dimension 2 à énergie fixe. Nous commençons par étudier une classe spéciale de solutions rationnelles non singulières de l'équation de Novikov-Veselov à énergie positive, construites par Grinevich et Zakharov, et nous démontrons que ces solutions sont multisolitons. Les solutions de Grinevich-Zakharov sont localisées comme $$ O( | x |^{ -2 } ) $$, $
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37

Kazeykina, Anna. "Solitons and large time asymptotics of solutions for the Novikov-Veselov equation." Palaiseau, Ecole polytechnique, 2012. http://pastel.archives-ouvertes.fr/docs/00/76/26/62/PDF/these.pdf.

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Ce travail est consacré à l'étude de l'équation de Novikov-Veselov, un analogue ( 2 + 1 )-dimensionnel de l'équation renommée de Korteweg-de Vries, intégrable via la transformée de la diffusion inverse pour l'équation de Schrödinger stationnaire en dimension 2 à énergie fixe. Nous commençons par étudier une classe spéciale de solutions rationnelles non singulières de l'équation de Novikov-Veselov à énergie positive, construites par Grinevich et Zakharov, et nous démontrons que ces solutions sont multisolitons. Les solutions de Grinevich-Zakharov sont localisées comme $$ O( | x |^{ -2 } ) $$, $
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38

Correa, Rafael Augusto Couceiro. "Estudo de sistemas não lineares em teoria de campos em baixas dimensões /." Guaratinguetá : [s.n.], 2010. http://hdl.handle.net/11449/99355.

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Orientador: Alvaro de Souza Dutra<br>Banca: Julio Marny Hoff da Silva<br>Banca: Bruto Max Pimentel Escobar<br>Resumo: Neste trabalho, apresentamos uma breve introdução ao estudo dos sólitons. Além disso, introduzimos uma nova classe de configurações oscilantes do tipo lump e do tipo kink. Tais configurações são obtidas de forma analítica e exata, como conseqüência somos capazes de fazer a análise da estabilidade das soluções apresentadas. Por fim, apresentamos no último capítulo soluções de estados ligados de férmions na presença das novas configurações de campo que estamos apresentando neste
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39

Kazeykina, Anna. "Solitons et comportement asymptotique des solutions en grand temps pour l'équation de Novikov-Veselov." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00762662.

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Ce travail est consacré à l'étude de l'équation de Novikov-Veselov, un analogue ( 2 + 1 )-dimensionnel de l'équation renommée de Korteweg-de Vries, intégrable via la transformée de la diffusion inverse pour l'équation de Schrödinger stationnaire en dimension 2 à énergie fixe. Nous commençons par étudier une classe spéciale de solutions rationnelles non singulières de l'équation de Novikov-Veselov à énergie positive, construites par Grinevich et Zakharov, et nous démontrons que ces solutions sont multisolitons. Les solutions de Grinevich-Zakharov sont localisées comme $ O( | x |^{ -2 } ) $, $ |
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40

Zaiter, Ibtissame. "Sur quelques équations dispersives." Paris 11, 2007. http://www.theses.fr/2007PA112247.

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Dans le cadre de ma thèse , on a étudié quelques types d'équations dispersives telles que le système de Boussinesq, l'équation de Benjamin et l'équation d'Ostrovsky. On démontre quelques résultats d'existence et de non existence du problème de Cauchy associé à un cas particulier du système de Boussinesq. Pour l'équation de Benjamin, on traite le caractère mal posé du problème de Cauchy ainsi que la contrainte de masse nulle. Un deuxième but est d'étudier les ondes solitaires: existence, non existence, régularité, symétrie, comportement à l'infini et convergence vers les ondes solitaires de l'é
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41

ROCHA, RENATA A. "Obtencao e caracterizacao de eletrolitos solidos de ceria-gadolinia." reponame:Repositório Institucional do IPEN, 2001. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10952.

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Made available in DSpace on 2014-10-09T12:46:00Z (GMT). No. of bitstreams: 0<br>Made available in DSpace on 2014-10-09T14:05:08Z (GMT). No. of bitstreams: 0<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Dissertacao (Mestrado)<br>IPEN/D<br>Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP<br>FAPESP:99/12494-9
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42

Menesguen, Yves. "Motifs transverses et solitons de cavité dans des microrésonateurs à semiconducteurs pompés optiquement." Paris 6, 2006. http://www.theses.fr/2006PA066065.

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43

Kong, Cho-wing Otto, and 江祖永. "K-DV solutions as quantum potentials: isospectral transformations as symmetries and supersymmetries." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B3120921X.

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44

Côte, Raphaël. "Construction et propriétés de solutions pour des équations dispersives focalisantes." Cergy-Pontoise, 2006. http://www.theses.fr/2006CERG0298.

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Dans cette thèse, nous étudions quelques propriétés de solutions d'équations aux dérivées partielles dispersives focalisantes. On étudie deux types d'équations. Dans un premier temps, nous étudions les équations de Korteweg-de Vries généralisées (gKdV). Étant donnée une solution de l'équation de Korteweg-de Vries linéaire, nous construisons une solution de (gKdV) qui se comporte ainsi pour des temps grands. Étant également donnés N solitons (ondes solitaires solutions de (gKdV)), nous construisons, dans les cas L2-critique et sous-critique, une solution de (gKdV) se comportant comme la somme d
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45

CAPRONI, ERICA. "Preparacao de eletrolitos solidos ceramicos de zirconia estabilizada com calcia." reponame:Repositório Institucional do IPEN, 2003. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11097.

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Made available in DSpace on 2014-10-09T12:48:18Z (GMT). No. of bitstreams: 0<br>Made available in DSpace on 2014-10-09T13:57:08Z (GMT). No. of bitstreams: 1 09307.pdf: 3599752 bytes, checksum: c720dc7c7bbb65919b1861882ea4796e (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Dissertacao (Mestrado)<br>IPEN/D<br>Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP<br>FAPESP:01/08029-0
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46

Feng, Zhaosheng. "Some results on the 1D linear wave equation with van der Pol type nonlinear boundary conditionsand the Korteweg-de Vries-Burgers equation." Diss., Texas A&M University, 2004. http://hdl.handle.net/1969.1/1078.

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Many physical phenomena can be described by nonlinear models. The last few decades have seen an enormous growth of the applicability of nonlinear models and of the development of related nonlinear concepts. This has been driven by modern computer power as well as by the discovery of new mathematical techniques, which include two contrasting themes: (i) the theory of dynamical systems, most popularly associated with the study of chaos, and (ii) the theory of integrable systems associated, among other things, with the study of solitons. In this dissertation, we study two nonlinear models. One i
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47

Floratos, Ioannis. "Multi-Skyrmion solutions of a sixth order Skyrme model." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3988/.

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In this Thesis, we study some of the classical properties of an extension of the Skyrme model defined by adding a sixth order derivative term to the Lagrangian. In chapter 1, we review the physical as well as the mathematical motivation behind the study of the Skyrme model and in chapter 2, we give a brief summary of various extended Skyrme models that have been proposed over the last few years. We then define a new sixth order Skyrme model by introducing a dimensionless parameter λ that denotes the mixing between the two higher order terms, the Skyrme term and the sixth order term. In chapter
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48

Cabrera, Carnero Iraida [UNESP]. "Modelos integráveis multicarregados e integrabilidade no plano não comutativo." Universidade Estadual Paulista (UNESP), 2003. http://hdl.handle.net/11449/102515.

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Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-02Bitstream added on 2014-06-13T20:23:07Z : No. of bitstreams: 1 cabreracarnero_i_dr_ift.pdf: 1015322 bytes, checksum: 915c6683e6c1c022f54ca1d9f5a03904 (MD5)<br>Nesta fase construísmo e estudamos uma nova classe de modelos integráveis (relativístico e não relativístico) em duas dimensões, associados à álgebra afim 'A IND.3 POT.(1)'. Estes modelos apresentam sólitons tipológicos os quais portam duas cargas elétricas U(1) X U(1). O modelo de Toda afim (relativístico) é construído a partir do
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49

Kalla, Caroline. "Fay's identity in the theory of integrable systems." Phd thesis, Université de Bourgogne, 2011. http://tel.archives-ouvertes.fr/tel-00622289.

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Fay's identity on Riemann surfaces is a powerful tool in the context of algebro-geometric solutions to integrable equations. This relation generalizes a well-known identity for the cross-ratio function in the complex plane. It allows to establish relations between theta functions and their derivatives. This offers a complementary approach to algebro-geometric solutions of integrable equations with certain advantages with respect to the use of Baker-Akhiezer functions. It has been successfully applied by Mumford et al. to the Korteweg-de Vries, Kadomtsev-Petviashvili and sine-Gordon equations.
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50

Vassenet, Marc-Antoine. "Étude des équations d’Euler-Korteweg." Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. https://theses.hal.science/tel-04678044.

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Dans cette thèse nous nous intéressons à divers aspect de l'équation d'Euler-Korteweg, équation de la mécanique des fluides. Dans un premier temps nous étudions la convergence des solitons dans la limite transonique vers les solutions de l'équation de Kadomstev-Petishveveli, après changement d'échelle en dimension deux. Ensuite, toujours en dimension deux nous étudions la stabilité des solutions de l'équation quantique d'Euler, à l'aide de la transformée de Madelung. Finalement dans la dernière partie nous étudions la limite des solutions quand la capillarité tend vers 0, sur tout l'espace et
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