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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_318749 |
| Date | January 1991 |
| Contributors | Zheng, Yu-kun., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, [vi], 140 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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