by Li Kam Shun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (p. 76). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

In this thesis we prove polynomial-in-time upper bounds for the orbital instability of solitons for subcritical generalized Korteweg-de Vries equations in $H^{s}_{x}(\mathbb{R})$ with $s < 1$. By combining coercivity estimates of Weinstein with the $I$-method as developed by Colliander, Keel, Staffilani, Takaoka, and Tao, we construct a modified energy functional which is shown to be almost conserved while providing us with an estimate of the deviation of the solution from the ground state curve. The iteration of the almost conservation law for the modified energy functional over time intervals of uniform length yields the polynomial upper bound.

In this thesis we prove polynomial-in-time upper bounds for the orbital instability of solitons for subcritical generalized Korteweg-de Vries equations in $H^{s}_{x}(\mathbb{R})$ with $s < 1$. By combining coercivity estimates of Weinstein with the $I$-method as developed by Colliander, Keel, Staffilani, Takaoka, and Tao, we construct a modified energy functional which is shown to be almost conserved while providing us with an estimate of the deviation of the solution from the ground state curve. The iteration of the almost conservation law for the modified energy functional over time intervals of uniform length yields the polynomial upper bound.

Thesis (Ph. D.)--Oregon State University, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 73-75). Also available on the World Wide Web.

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Thesis (M.Sc.) - Carleton University, 2006. / Includes bibliographical references (p. 54-55). Also available in electronic format on the Internet.

Thesis (M.Sc.) - Carleton University, 2007. / Includes bibliographical references (p. 103-106). Also available in electronic format on the Internet.

No description available.

by Li Kam Shun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaf 65). / Chapter CHAPTER 1 --- Soliton Solutions of the Nonisospectral and Variable Coefficient Korteweg-de Vries Equation / Chapter §1.1 --- Introduction --- p.4 / Chapter §1.2 --- Inverse Scattering --- p.6 / Chapter §1.3 --- N-Soliton Solution --- p.11 / Chapter §1.4 --- One-Soliton Solutions --- p.15 / Chapter §1.5 --- Two-Soliton Solutions --- p.18 / Chapter §1.6 --- Oscillating and Asymptotically Standing Solitons --- p.23 / Chapter CHAPTER 2 --- Asymptotic Behaviour of Nonsoliton Solutions of the Nonisospectral and Variable Coefficient Korteweg-de Vries Equation / Chapter §2.1 --- Introduction --- p.31 / Chapter §2.2 --- Main Results --- p.36 / Chapter §2.3 --- Lemmas --- p.39 / Chapter §2.4 --- Proof of the Main Results --- p.59 / References --- p.65

Zhou Yong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 51-53). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.2 / Chapter 2 --- Preliminaries --- p.10 / Chapter 3 --- Periodic Case --- p.22 / Chapter 4 --- Non-periodic Case --- p.35 / Bibliography --- p.51