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Dissertations / Theses on the topic 'Nonlinear systems of equations'

Author: Grafiati

Published: 10 March 2023

Last updated: 25 July 2025

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1

Hadad, Yaron. "Integrable Nonlinear Relativistic Equations." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293490.

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This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to the Sinh-Gordon equation. For the 1+1 E

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2

Zerihun, Tadesse G. "Nonlinear Techniques for Stochastic Systems of Differential Equations." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4970.

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Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematical

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3

Jaschke, Leonhard. "Preconditioned Arnoldi methods for systems of nonlinear equations /." Paris (121 Av. des Champs-Élysées, 75008) : Wiku, 2004. http://catalogue.bnf.fr/ark:/12148/cb391991990.

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4

Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.

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5

Van, der Walt Jan Harm. "Generalized solutions of systems of nonlinear partial differential equations." Thesis, Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-05242009-122628.

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6

Reichelt, Sina. "Two-scale homogenization of systems of nonlinear parabolic equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17385.

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Ziel dieser Arbeit ist es zwei verschiedene Klassen von Systemen nichtlinearer parabolischer Gleichungen zu homogenisieren, und zwar Reaktions-Diffusions-Systeme mit verschiedenen Diffusionslängenskalen und Gleichungen vom Typ Cahn-Hilliard. Wir betrachten parabolische Gleichungen mit periodischen Koeffizienten, wobei die Periode dem Verhältnis der charakteristischen mikroskopischen zu der makroskopische Längenskala entspricht. Unser Ziel ist es, effektive Gleichungen rigoros herzuleiten, um die betrachteten Systeme besser zu verstehen und den Simulationsaufwand zu minimieren. Wir suchen a

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7

Alam, Md Shafiful. "Iterative Methods to Solve Systems of Nonlinear Algebraic Equations." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2305.

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Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the

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8

Handel, Andreas. "Limits of Localized Control in Extended Nonlinear Systems." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5025.

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We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance

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9

Twiton, Michael. "Analysis of Singular Solutions of Certain Painlevé Equations." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18206.

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The six Painlevé equations can be described as the boundary between the non- integrable- and the trivially integrable-systems. Ever since their discovery they have found numerous applications in mathematics and physics. The solutions of the Painlevé equations are, in most cases, highly transcendental and hence cannot be expressed in closed form. Asymptotic methods do better, and can establish the behaviour of some of the solutions of the Painlevé equations in the neighbourhood of a singularity, such as the point at infinity. Although the quantitative nature of these neighbourhoods is not initi

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10

Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

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11

Floater, Michael S. "Blow-up of solutions to nonlinear parabolic equations and systems." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235037.

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12

Craciun, Gheorghe. "Systems of nonlinear equations deriving from complex chemical reaction networks /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486463321624709.

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13

Zhelezov, Gleb, and Gleb Zhelezov. "Coalescing Particle Systems and Applications to Nonlinear Fokker-Planck Equations." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/624562.

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We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping. We show that when the system is in an appropriate parameter regime, the hydrodynamic limit of the empirical mass density of the system is a solution to a nonlinear Fokker-Planck equation,

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14

Wu, Xiaoming. "Partial differential equations with applications to wave propagation." Thesis, University of Newcastle Upon Tyne, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239573.

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15

Leiva, Hugo. "Skew-product semiflows and time-dependent dynamical systems." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/29912.

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16

Rejoub, Riad A. "Projective and non-projective systems of first order nonlinear differential equations." Scholarly Commons, 1992. https://scholarlycommons.pacific.edu/uop_etds/2228.

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It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait. In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas] The xi may generally be consider

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17

See, Chong Wee Simon. "Numerical methods for the simulation of dynamic discontinuous systems." Thesis, University of Salford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358276.

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18

Klug, Andreas. "Affine-scaling methods for nonlinear minimization problems and nonlinear systems of equations with bound constraints." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981743978.

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19

Mulvey, Joseph Anthony. "Symmetry methods for integrable systems." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5379/.

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This thesis discusses various properties of a number of differential equations which we will term "integrable". There are many definitions of this word, but we will confine ourselves to two possible characterisations — either an equation can be transformed by a suitable change of variables to a linear equation, or there exists an infinite number of conserved quantities associated with the equation that commute with each other via some Hamiltonian structure. Both of these definitions rely heavily on the concept of the symmetry of a differential equation, and so Chapters 1 and 2 introduce and ex

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20

Gurevich, Svetlana V. "Lateral self-organization in nonlinear transport systems described by reaction diffusion equations." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=983706921.

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21

Philipowski, Robert. "Stochastic interacting particle systems and nonlinear partial differential equations from fluid mechanics." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=986005622.

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22

Joubert, Adriaan Wolfgang. "Parallel methods for systems of nonlinear equations applied to load flow analysis." Thesis, Queen Mary, University of London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362721.

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23

Bobade, Parag Suhas. "Modeling, Approximation, and Control for a Class of Nonlinear Systems." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/80978.

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This work investigates modeling, approximation, estimation, and control for classes of nonlinear systems whose state evolves in space $mathbb{R}^n times H$, where $mathbb{R}^n$ is a n-dimensional Euclidean space and $H$ is a infinite dimensional Hilbert space. Specifically, two classes of nonlinear systems are studied in this dissertation. The first topic develops a novel framework for adaptive estimation of nonlinear systems using reproducing kernel Hilbert spaces. A nonlinear adaptive estimation problem is cast as a time-varying estimation problem in $mathbb{R}^d times H$. In contrast to mo

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24

Ali, Jaffar. "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects." Diss., Mississippi State : Mississippi State University, 2008. http://library.msstate.edu/etd/show.asp?etd=etd-07082008-153843.

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25

Ye, Jinglong. "Infinite semipositone systems." Diss., Mississippi State : Mississippi State University, 2009. http://library.msstate.edu/etd/show.asp?etd=etd-07072009-132254.

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26

Ahlip, Rehez Ajmal. "Stability & filtering of stochastic systems." Thesis, Queensland University of Technology, 1997.

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27

O'Day, Joseph Patrick. "Investigation of a coupled Duffing oscillator system in a varying potential field /." Online version of thesis, 2005. https://ritdml.rit.edu/dspace/handle/1850/1212.

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28

Clinger, Richard A. "Stability Analysis of Systems of Difference Equations." VCU Scholars Compass, 2007. http://hdl.handle.net/10156/1318.

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29

Marahrens, Daniel. "On some nonlinear partial differential equations for classical and quantum many body systems." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/244203.

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This thesis deals with problems arising in the study of nonlinear partial differential equations arising from many-body problems. It is divided into two parts: The first part concerns the derivation of a nonlinear diffusion equation from a microscopic stochastic process. We give a new method to show that in the hydrodynamic limit, the particle densities of a one-dimensional zero range process on a periodic lattice converge to the solution of a nonlinear diffusion equation. This method allows for the first time an explicit uniform-in-time bound on the rate of convergence in the hydrodynamic lim

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30

Taylor, Gillian Clare. "Application of the Hodgkin-Huxley equations to the propagation of small graded potentials in neurons." Thesis, Heriot-Watt University, 1996. http://hdl.handle.net/10399/742.

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31

Khames, Imene. "Nonlinear network wave equations : periodic solutions and graph characterizations." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR04/document.

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Dans cette thèse, nous étudions les équations d’ondes non-linéaires discrètes dans des réseaux finis arbitraires. C’est un modèle général, où le Laplacien continu est remplacé par le Laplacien de graphe. Nous considérons une telle équation d’onde avec une non-linéarité cubique sur les nœuds du graphe, qui est le modèle φ4 discret, décrivant un réseau mécanique d’oscillateurs non-linéaires couplés ou un réseau électrique où les composantes sont des diodes ou des jonctions Josephson. L’équation d’onde linéaire est bien comprise en termes de modes normaux, ce sont des solutions périodiques associ

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32

Zhang, Xiaohong. "Optimal feedback control for nonlinear discrete systems and applications to optimal control of nonlinear periodic ordinary differential equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40185.

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33

Steinhauer, Mark. "On analysis of some nonlinear systems of partial differential equations of continuum mechanics." Bonn : Mathematisches Institut der Universität, 2003. http://catalog.hathitrust.org/api/volumes/oclc/54890745.html.

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34

Chen, Yahao. "Geometric analysis of differential-algebraic equations and control systems : linear, nonlinear and linearizable." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR04.

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Dans la première partie de cette thèse, nous étudions les équations différentielles algébriques (en abrégé EDA) linéaires et les systèmes de contrôles linéaires associés (en abrégé SCEDA). Les problèmes traités et les résultats obtenus sont résumés comme suit : 1. Relations géométriques entre les EDA linéaires et les systèmes de contrôles génériques SCEDO. Nous introduisons une méthode, appelée explicitation, pour associer un SCEDO à n'importe quel EDA linéaire. L'explicitation d'une EDA est une classe des SCEDO, précisément un SCEDO défini, à un changement de coordonnées près, une transformat

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35

Zhang, Jin. "Identification of nonlinear structural dynamical system." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/12270.

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36

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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37

Chan, Chuen Lit. "A perturbation-incremental (PI) method for strongly non-linear oscillators and systems of delay differential equations /." access full-text access abstract and table of contents, 2005. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b1988767xa.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2005.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy" Includes bibliographical references (leaves 121-133)

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38

Lazaryan, Shushan, Nika LAzaryan, and Nika Lazaryan. "Discrete Nonlinear Planar Systems and Applications to Biological Population Models." VCU Scholars Compass, 2015. http://scholarscompass.vcu.edu/etd/4025.

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We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential. We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of line

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39

Nersesov, Sergey G. "Nonlinear Impulsive and Hybrid Dynamical Systems." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7147.

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Modern complex dynamical systems typically possess a multiechelon hierarchical hybrid structure characterized by continuous-time dynamics at the lower-level units and logical decision-making units at the higher-level of hierarchy. Hybrid dynamical systems involve an interacting countable collection of dynamical systems defined on subregions of the partitioned state space. Thus, in addition to traditional control systems, hybrid control systems involve supervising controllers which serve to coordinate the (sometimes competing) actions of the lower-level controllers. A subclass of hybrid dynamic

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40

Zhao, Yaxi. "Numerical solutions of nonlinear parabolic problems using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/zhaoy/yaxizhao.pdf.

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41

Pereira, da Silva João Gustavo [Verfasser]. "Modelling Flash Sintering Using Systems of Nonlinear Differential Equations / João Gustavo Pereira da Silva." München : Verlag Dr. Hut, 2019. http://d-nb.info/1190421836/34.

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42

Sakurai, Atsunori. "Exploring Nonlinear Responses of Quantum Dissipative Systems from Reduced Hierarchy Equations of Motion Approach." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/179368.

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43

Yang, Lixiang. "Modeling Waves in Linear and Nonlinear Solids by First-Order Hyperbolic Differential Equations." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1303846979.

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44

Gerdin, Markus. "Identification and Estimation for Models Described by Differential-Algebraic Equations." Doctoral thesis, Linköping : Department of Electrical Engineering, Linköpings universitet, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7600.

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45

Cimen, Tayfun. "Global optimal feedback control of nonlinear systems and viscosity solutions of Hamilton-Jacobi-Bellman equations." Thesis, University of Sheffield, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289660.

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46

Smith, Todd Blanton. "Variational embedded solitons, and traveling wavetrains generated by generalized Hopf bifurcations, in some NLPDE systems." Doctoral diss., University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5042.

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In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary w

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47

Gilmour, Isla. "Nonlinear model evaluation : ɩ-shadowing, probabilistic prediction and weather forecasting". Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298797.

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Physical processes are often modelled using nonlinear dynamical systems. If such models are relevant then they should be capable of demonstrating behaviour observed in the physical process. In this thesis a new measure of model optimality is introduced: the distribution of ɩ-shadowing times defines the durations over which there exists a model trajectory consistent with the observations. By recognising the uncertainty present in every observation, including the initial condition, ɩ-shadowing distinguishes model sensitivity from model error; a perfect model will always be accepted as optimal. T

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48

SOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.

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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variationa

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49

Durmaz, Burak. "Sliding Mode Control Of Linearly Actuated Nonlinear Systems." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610666/index.pdf.

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This study covers the sliding mode control design for a class of nonlinear systems, where the control input affects the state of the system linearly as described by (d/dt)x=A(x)x+B(x)u+d(x). The main streamline of the study is the sliding surface design for the system. Since there is no systematic way of designing sliding surfaces for nonlinear systems, a moving sliding surface is designed such that its parameters are determined in an adaptive manner to cope with the nonlinearities of the system. This adaptive manner includes only the automatic adaptation of the sliding surface by determining

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Bradley, Aoibhinn Maire. "Analysis of nonlinear spatio-temporal partial differential equations : applications to host-parasite systems and bubble growth." Thesis, University of Strathclyde, 2014. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=24405.

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The mountain hare population currently appears to be under threat in Scotland. The natural population cycles exhibited by this species are thought to be, at least in part, due to its infestation by a parasitic worm. We seek to gain an understanding of these population dynamics through a mathematical model of this system and so determine whether low population levels observed in the field are a natural trough associated with this cycling, or whether they point to a more serious decline in overall population densities. A generic result, that can be used to predict the presence of periodic travel

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