In this paper we construct explicit examples of solutions to certain nonlinear wave equations. These semilinear equations are the simplest equations known to possess localized solitary waves in more that one spatial dimension. We construct explicit localized standing wave solutions, which generate multidimensional localized traveling solitary waves under the action of velocity boosts. We study the case of two spatial dimensions and a piecewise-linear nonlinearity. We obtain a large subset of the infinite family of standing waves, and we exhibit several interesting features of the family. Our solutions include solitary waves that carry nonzero angular momenta in their rest frames. The spatial profiles of these solutions also furnish examples of symmetry breaking for nonlinear elliptic equations.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504381 |
| Date | 08 1900 |
| Creators | King, Gregory B. (Gregory Blaine) |
| Contributors | Warchall, Henry Alexander, Neuberger, John W. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | vii, 147 leaves: ill., Text |
| Rights | Public, King, Gregory B. (Gregory Blaine), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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