Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media

Luna, Manuel

Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media

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Type

Thesis

Turkiyyah, George

Program

Applied Mathematics and Computational Science

KAUST Department

Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

Date

2011-05

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.

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