No description available.

Thesis (Ph. D.)--University of Hong Kong, 1989.

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

No description available.

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 22, 2009) Vita. Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 60-62).

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009. / Title from title screen (site viewed January 5, 2010). PDF text: vi, 157 p. : ill. ; 2 Mb. UMI publication number: AAT 3360085. Includes bibliographical references. Also available in microfilm and microfiche formats.

by Zheng Yu-kun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Preface --- p.1 / Chapter Chapter 1. --- Gauge Transformation and the Higher Order Korteweg-de Vries Equations --- p.6 / Chapter 1. --- Higher order KdV equations --- p.6 / Chapter 2. --- η2-dependent higher order mKdV equations --- p.9 / Chapter 3. --- η2-dependent Miura transformation and Backlund transformation --- p.13 / Chapter 4. --- Gauge transformation of the wave function --- p.15 / Chapter 5. --- Backlund transformation for the η2 -dependent higher order mKdV equation --- p.24 / Chapter 6. --- Applications --- p.25 / Chapter 7. --- References --- p.30 / Chapter Chapter 2. --- Solutions of a Nonisospectral and Variable Coefficient Korteweg-de Vries Equation --- p.31 / Chapter 1. --- Introduction --- p.31 / Chapter 2. --- Nonisospectral variable coefficient KdV-type equations --- p.32 / Chapter 3. --- Invariance of LP under the Crum transformation --- p.34 / Chapter 4. --- Backlund transformation for the h-t-KdV equation --- p.35 / Chapter 5. --- Solutions --- p.39 / Chapter 6. --- References --- p.43 / Chapter Chapter 3. --- Nonisospectral Variable Coefficient Higher Order Korteweg-de Vries Equations --- p.45 / Chapter 1. --- Introduction --- p.45 / Chapter 2. --- Nonisospectral t-ho-KdV equations --- p.47 / Chapter 3. --- Nonisospectral η2 dependent variable coefficient higher order modified KdV equation --- p.50 / Chapter 4. --- Backlund transformation and gauge transformation --- p.57 / Chapter 5. --- Example. Solutions of second order ni-t-KdV equation and its corresponding ni-t-η2-mKdV equation --- p.61 / Chapter 6. --- References --- p.66 / Chapter Chapter 4. --- Gauge and Backlund Transformations for the Variable Coefficient Higher-Order Modified Korteweg-de Vries Equation --- p.67 / Chapter 1. --- Introduction --- p.67 / Chapter 2. --- The t-ho-mKdV equation --- p.68 / Chapter 3. --- Some results about the t-ho-KdV equation --- p.74 / Chapter 4. --- A Backlund transformation for the t-ho-mKdV equation --- p.76 / Chapter 5. --- Gauge transformat ion and the Backlund transformation --- p.78 / Chapter 6. --- References --- p.85 / Chapter Chapter 5. --- Gauge and Backlund Transformat ions for the Generalized Sine-Gordon Equation and Its η Dependent Modified Equation --- p.86 / Chapter 1. --- Introduction --- p.86 / Chapter 2. --- Generalized Sine-Gordon equation --- p.87 / Chapter 3. --- Backlund transformation for the GSGE --- p.92 / Chapter 4. --- Gauge transformations for AKNS systems --- p.98 / Chapter 5. --- η dependent modified GSGE and its Backlund transformation --- p.102 / Chapter 6. --- Summary and example --- p.105 / Chapter 7. --- References --- p.110 / Chapter Chapter 6. --- Backlund Transformation for the Nonisospectral and Variable Coefficient Nonlinear Schrodinger Equation --- p.111 / Chapter 1. --- Introduction --- p.111 / Chapter 2. --- A generalized NLSE --- p.112 / Chapter 3. --- Γ Riccati equation system --- p.114 / Chapter 4. --- Invariance of the Γ-system --- p.116 / Chapter 5. --- Lax pair corresponding to the GNLSE --- p.119 / Chapter 6. --- BT´ةs for the Γ evolution equation and the GNLSE --- p.121 / Chapter 7. --- References --- p.126 / Chapter Chapter 7. --- Backlund Transformations for the Caudrey-Dodd-Gibbon-Sawada-Kotera Equation and Its λ-Modified Equation --- p.127 / Chapter 1. --- Introduction --- p.127 / Chapter 2. --- The CDGSKE and the λ-mCDGSKE --- p.128 / Chapter 3. --- The general solution for the scattering problem of the CDGSKE --- p.130 / Chapter 4. --- The BT for the λ-mCDGSKE --- p.135 / Chapter 5. --- The BT for the CDGSKE --- p.136 / Chapter 6. --- References --- p.139 / Summary --- p.140

In this work, we study the Hull-Strominger system. New solutions are found on hyperkahler fibrations over a Riemann surface. This class of solutions is the first which admits infinitely many topological types. Next, we study the Fu-Yau solutions of the Hull-Strominger system and their generalizations to higher dimensions. We solve the Fu-Yau equation in higher dimensions, and in fact, solve a new class of fully nonlinear elliptic PDE which contains the Fu-Yau equation as a special case. Lastly, we introduce a geometric flow to study the Hull-Strominger system and non-Kahler Calabi-Yau threefolds. Basic properties are established, and we study this flow in the geometric settings of fibrations over a Riemann surface and fibrations over a K3 surface. In both cases, the flow descends to a nonlinear evolution equation for a scalar function on the base, and we study the dynamical behavior of these evolution equations.