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.
| Date of Award | May 2011 |
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| Original language | English (US) |
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| Awarding Institution | - Computer, Electrical and Mathematical Sciences and Engineering
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| Supervisor | David Ketcheson (Supervisor) |
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