Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Aug. 14, 2008). PDF text: vi, 118 p. ; 460 K. UMI publication number: AAT 3297658. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (PhD) - Swinburne University of Technology, Faculty of Engineering and Industrial Sciences, 2008. / A thesis presented for the degree of Doctor of Philosophy, Mathematics discipline, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, 2008. Typescript. Bibliography: p. 245-259.

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

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaf 136). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--Oregon State University, 1991. / Typescript (photocopy). Includes bibliographical references (leaves 62-64). Also available on the World Wide Web.

In chapter 2 we use functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schrodinger equation for initial data that satisfy some suitable conditions. In chapter 3 we use the energy estimates to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H³(R) as ε → 0; also, we show that the strong L²(R)-limit of the solutions of the BBM equation as ε → 0 before a critical time. In chapter 4 we use the Whitham modulation theory and averaging method to find the 2π-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. We show that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, we study the relations of the KdV equation and the mKdV equation. Finally, we study the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.

146 leaves : tables ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics, 1979

Thesis (Ph.D.) -- University of Adelaide, Department of Mathematical Physics, 1979.

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