Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
dc.contributor.advisor | Ketcheson, David I. | |
dc.contributor.author | Luna, Manuel | |
dc.date.accessioned | 2012-02-04T08:42:50Z | |
dc.date.available | 2012-02-04T08:42:50Z | |
dc.date.issued | 2011-05 | |
dc.identifier.citation | Luna, M. (2011). Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media. KAUST Research Repository. https://doi.org/10.25781/KAUST-51374 | |
dc.identifier.doi | 10.25781/KAUST-51374 | |
dc.identifier.uri | http://hdl.handle.net/10754/209415 | |
dc.description.abstract | Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general. | |
dc.language.iso | en | |
dc.title | Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media | |
dc.type | Thesis | |
dc.contributor.department | Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division | |
thesis.degree.grantor | King Abdullah University of Science and Technology | |
dc.contributor.committeemember | Kasimov, Aslan R. | |
dc.contributor.committeemember | Turkiyyah, George | |
thesis.degree.discipline | Applied Mathematics and Computational Science | |
thesis.degree.name | Master of Science | |
refterms.dateFOA | 2018-06-14T06:14:49Z |
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Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
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