En la presente inventigación prueba resultados de buena colocación global para la ecuación de Kortewegde Vries modificada en el espacio de Sobolev H2(R) usando los argumentos probados por A. V. Famiskii y basada en los argumentos presentados por Peter E. Zhidkov. / Tesis

This investigation is devoted to the study of the Fermi-Pasta-Ulam (FPU) lattice dynamics. Approximations of the FPU lattice dynamics have been an old subject, it is believed that the stability of the FPU traveling waves depends on the stability of the KDV solitary waves. The key question is: Are the traveling waves of the FPU lattice stable if the traveling waves of KDV type equation are stable?. We consider the FPU lattice with the nonlinear potential which leads to the generalized Korteweg-de Vries (gKDV) equation, which is known to have orbitally stable traveling waves in a subcritical case and orbitally unstable traveling waves in critical and supercritical cases. In order to pursue the question asked above, we use the energy method. We establish that the H^s(R) norm of the solution of the gKDV equation is bounded by a time-independent constant in the subcritical case, whereas the H^s(R) norm grows at most exponentially in the critical and supercritical cases. With the help of these results, we extend the time scale for the approximation of the traveling waves of the FPU lattice by the traveling waves of the gKDV equation logarithmically in the subcritical case. In the critical and supercritical cases, we extend the time scale by a double-logarithmic factor. Our results show that the traveling waves of the FPU lattice are stable if the solitary waves of the gKDV equation are stable in the subcritical case. On the other hand, in the critical and supercritical cases, our results are restricted to small-norm initial data, which exclude solitary waves. / Thesis / Master of Science (MSc)

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Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

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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

Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

published_or_final_version / Physics / Master / Master of Philosophy