Approximate Solution of the Kuramoto-Shivashinsky Equation on an Unbounded Domain |
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Authors: | Wael W MOHAMMED |
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Institution: | 1.Department of Mathematics, Faculty of Science,Mansoura University,Mansoura,Egypt;2.Department of Mathematics, Faculty of Science,Hail University,Hail,Saudi Arabia |
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Abstract: | The main goal of this paper is to approximate the Kuramoto-Shivashinsky (K-S for short) equation on an unbounded domain near a change of bifurcation, where a band of dominant pattern is changing stability. This leads to a slow modulation of the dominant pattern. Here we consider PDEs with quadratic nonlinearities and derive rigorously the modulation equation, which is called the Ginzburg-Landau (G-L for short) equation, for the amplitudes of the dominating modes. |
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Keywords: | Multi-scale analysis Modulation equation Kuramoto-Shivashinsky equation Ginzburg-Landau equation |
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