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dc.contributor.advisorKetcheson, David I.
dc.contributor.authorLuna, Manuel
dc.date.accessioned2012-02-04T08:42:50Z
dc.date.available2012-02-04T08:42:50Z
dc.date.issued2011-05
dc.identifier.citationLuna, 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.doi10.25781/KAUST-51374
dc.identifier.urihttp://hdl.handle.net/10754/209415
dc.description.abstractSolitary 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.isoen
dc.titleNonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberKasimov, Aslan R.
dc.contributor.committeememberTurkiyyah, George
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science
refterms.dateFOA2018-06-14T06:14:49Z


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