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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/185840 |
| Date | January 1992 |
| Creators | Tso, Taicheng. |
| Contributors | Levermore, C. David, Palmer, John, Greenlee, W. Martin |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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