Dissertation (Ph.D. in Applied Mathematics)--Naval Postgraduate School, June 2010. / Dissertation supervisor(s): Neta, Beny ; Giraldo, Francis. "June 2010." Description based on title screen as viewed on July 15, 2010. Author(s) subject terms: Non-reflecting Boundary, Spectral Elements, Runge-Kutta, High-Order, Klein-Gordon, Shallow Water Equations. Includes bibliographical references (p. 145-150). Also available in print.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 126-131). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 152-162). Available also in a digital version from Dissertation Abstracts.

It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin parallel or antiparallel to the magnetic field direction.

Lee Joy Yan Agatha. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [112]-114). / Text in English; abstracts in English and Chinese. / Lee Joy Yan Agatha. / Abstract --- p.ii / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.viii / List of Tables --- p.xii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- The Transfer Integral Equation Method --- p.3 / Chapter 2.1 --- The System --- p.3 / Chapter 2.1.1 --- The Hamiltonian --- p.4 / Chapter 2.1.2 --- The length parameter --- p.5 / Chapter 2.1.3 --- The temperature parameter --- p.5 / Chapter 2.2 --- The Transfer Integral Equation --- p.6 / Chapter 2.2.1 --- The partition function --- p.6 / Chapter 2.2.2 --- The transfer integral equation --- p.6 / Chapter 2.2.3 --- The pseudo-Schrodinger equation approximation --- p.7 / Chapter 2.2.4 --- Distribution function of the displacements --- p.9 / Chapter 2.3 --- The Thermodynamics --- p.10 / Chapter 2.3.1 --- Internal energy and heat capacity --- p.10 / Chapter 2.3.2 --- Displacement fluctuation --- p.12 / Chapter 2.3.3 --- Displacement correlation function --- p.12 / Chapter Chapter 3. --- The Φ4 Chain --- p.14 / Chapter 3.1 --- Soliton In The Chain --- p.15 / Chapter 3.1.1 --- Kink soliton and antikink soliton --- p.15 / Chapter 3.1.2 --- Energy of a static kink --- p.18 / Chapter 3.2 --- Low Temperature WKB Approximation for the Φ4 Chain --- p.20 / Chapter 3.2.1 --- The ground state energy ε0 and tunneling-splitting contribution --- p.20 / Chapter 3.2.2 --- First order WKB approximation of ΨRo( φ) --- p.22 / Chapter 3.2.3 --- Second order WKB wavefunction ΨRo( φ)） --- p.26 / Chapter 3.2.4 --- Third order WKB wavefunction for ΨRo( φ) --- p.27 / Chapter 3.3 --- Thermodynamics --- p.28 / Chapter 3.3.1 --- Ground state energy ε0 and wavefunction Ψo( φ) --- p.28 / Chapter 3.3.2 --- Internal energy and heat capacity --- p.33 / Chapter 3.3.3 --- Displacement correlation function --- p.36 / Chapter Chapter 4. --- Other Nonlinear Klein-Gordon Models --- p.42 / Chapter 4.1 --- The φ8 Chain --- p.42 / Chapter 4.1.1 --- The potential --- p.42 / Chapter 4.1.2 --- The ground state energy εo and wavefunction Ψo( φ) --- p.44 / Chapter 4.1.3 --- Internal energy and heat capacity --- p.49 / Chapter 4.1.4 --- Displacement correlation function cyy(n) --- p.51 / Chapter 4.2 --- The Gaussian-Double-Well Chains --- p.53 / Chapter 4.2.1 --- The potential --- p.53 / Chapter 4.2.2 --- The ground state energy εo and wavefunction ψo --- p.55 / Chapter 4.2.3 --- Internal energy and heat capacity --- p.58 / Chapter 4.2.4 --- Displacement correlation function cyy(n) --- p.59 / Chapter 4.3 --- Comparison Between Different NKG Models --- p.61 / Chapter 4.3.1 --- The potentials --- p.61 / Chapter 4.3.2 --- Ground state energy εo and wavefunction ψo(ψ) --- p.65 / Chapter 4.3.3 --- Internal energy and heat capacity --- p.68 / Chapter 4.3.4 --- Displacement fluctuation --- p.70 / Chapter 4.3.5 --- Displacement correlation function cyy(n) --- p.71 / Chapter 4.4 --- Linear Response of a NKG Chain to a Static Perturbing Field --- p.75 / Chapter 4.4.1 --- The external perturbing field --- p.75 / Chapter 4.4.2 --- The linear response --- p.75 / Chapter 4.4.3 --- Linear response of an array of weakly coupled NKG chains --- p.80 / Chapter Chapter 5. --- Quantum Corrections --- p.86 / Chapter 5.1 --- The Effective Potential --- p.86 / Chapter 5.1.1 --- The smearing parameter --- p.86 / Chapter 5.1.2 --- The effective potential --- p.88 / Chapter 5.2 --- Quantum Corrections on Thermodynamics --- p.90 / Chapter 5.2.1 --- The ground state energy εo and wavefunction ψo(ψ) --- p.90 / Chapter 5.2.2 --- The heat capacity --- p.94 / Chapter 5.2.3 --- Displacement correlation function and displacement fluctuation --- p.97 / Chapter Chapter 6. --- Conclusion --- p.103 / Appendix A. Infinite-Square-Well Basis Diagonalization --- p.105 / Appendix B. Oscillator Basis Diagonalization --- p.110 / Bibliography --- p.112

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010. / Committee Chair: Harrell, Evans; Committee Member: Chow, Shui-Nee; Committee Member: Geronimo, Jeffrey; Committee Member: Kennedy, Brian; Committee Member: Loss, Michael. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-12Bitstream added on 2014-06-13T19:47:26Z : No. of bitstreams: 1 arroyo_vc_me_sjrp.pdf: 221886 bytes, checksum: 7aff63436217938f6e748fdea1840581 (MD5) / Neste trabalho estudamos a equação de Klein-Gordon linear. Definimos solução generalizada do Problema de Cauchy para tal equação. Provamos a existência e a unicidade da solução no espaço H1 loc(R2 + 1) e demonstramos o decaimento local de energia da solução. / In this work we studdy the linear Klein-Gordon equation. We define the notion of generalized solution to the Cauchy problem for such equation. We prove existence and uniqueness of solution in H1 loc(R2 + 1). We also prove local decay of energy for the solutions to the Cauchy problem.

Orientador: Waldemar Donizete Bastos / Banca: Marcelo Reicher Soares / Banca: Juliana Conceição Precioso Pereira / Resumo: Neste trabalho estudamos a equação de Klein-Gordon linear. Definimos solução generalizada do Problema de Cauchy para tal equação. Provamos a existência e a unicidade da solução no espaço H1 loc(R2 + 1) e demonstramos o decaimento local de energia da solução. / Abstract: In this work we studdy the linear Klein-Gordon equation. We define the notion of generalized solution to the Cauchy problem for such equation. We prove existence and uniqueness of solution in H1 loc(R2 + 1). We also prove local decay of energy for the solutions to the Cauchy problem. / Mestre

This thesis presents a development of classical canonical formalism and the usual transition schema to quantum dynamics. The question of transition from relativistic mechanics to relativistic quantum dynamics is answered by developing a homogeneous formalism which is relativistically invariant. Using this formalism the Klein-Gordon equation is derived as the relativistic analog of the Schroedinger equation. Using this formalism further, a method of generating other relativistic equations (with spin) is presented.

Mak Ka Wai Charles. / Thesis submitted in: October 2001. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 89-91). / Text in English; abstracts in English and Chinese. / Mak Ka Wai Charles. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview of the Mathematical Framework --- p.2 / Chapter 1.2 --- System of Interest --- p.7 / Chapter 1.2.1 --- Klein-Gordon equation --- p.7 / Chapter 1.2.2 --- QNM boundary conditions --- p.12 / Chapter 1.3 --- Outline of This Thesis --- p.14 / Chapter 2 --- Green's Function --- p.15 / Chapter 2.1 --- "Formal Expression for G(x,y，w)" --- p.16 / Chapter 2.2 --- "Leaver's Series Solution: An Analytic Expression for g(r, w)" --- p.17 / Chapter 2.3 --- Location of the Cut --- p.22 / Chapter 2.4 --- "Jaffe's Series Solution: An Analytic Expression for f(r,w)" --- p.23 / Chapter 2.5 --- QNMs and Their Locations --- p.26 / Chapter 2.5.1 --- Alternative definitions of QNM --- p.26 / Chapter 2.5.2 --- Methods of searching for QNMs --- p.28 / Chapter 2.5.3 --- Locations of QNMs --- p.29 / Chapter 2.6 --- Green's Function and Eigenspectra --- p.30 / Chapter 3 --- Normalization Function: Analytical Treatment --- p.34 / Chapter 3.1 --- Definition and Properties --- p.34 / Chapter 3.2 --- Analytic Approximations for --- p.36 / Chapter 3.3 --- Polar Perturbations --- p.39 / Chapter 4 --- Normalization Function: Numerical Treatment --- p.42 / Chapter 4.1 --- "Numerical Algorithm for g(x,w)" --- p.42 / Chapter 4.1.1 --- Method --- p.42 / Chapter 4.1.2 --- Equation governing R(z) --- p.45 / Chapter 4.1.3 --- "Equations governing A(x, z) and B(x, z)" --- p.45 / Chapter 4.2 --- "Numerical Algorithm for g(x, ´ؤw)" --- p.49 / Chapter 4.3 --- Numerical Result of q(γ) --- p.50 / Chapter 4.4 --- Comparison of Numerical Result with Analytic Approximations --- p.56 / Chapter 5 --- "Branch Cut Strength of G(x, y, w)" --- p.58 / Chapter 5.1 --- "Relation between q(γ) and ΔG(x,y, ´ؤiγ)" --- p.58 / Chapter 5.2 --- Proof of the Power Law --- p.60 / Chapter 5.3 --- "Numerical Results for ΔG(x, y, ´ؤiγ)" --- p.63 / Chapter 5.4 --- Study of a Physically Important Limit --- p.65 / Chapter 5.4.1 --- Limiting x and y --- p.65 / Chapter 5.4.2 --- Poles on the unphysical sheet --- p.69 / Chapter 5.4.3 --- Zerilli potential --- p.77 / Chapter 6 --- Conclusion --- p.81 / Chapter A --- Tortoise Coordinate --- p.84 / Chapter B --- Solution of the Generalized Coulomb Wave Equation --- p.86 / Chapter C --- Derivation of (5.1) --- p.88 / Bibliography --- p.89