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Open AccessArticle

Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line

1
Department of mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2
Mathematics Department, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Mathematics 2019, 7(12), 1217; https://doi.org/10.3390/math7121217
Received: 17 November 2019 / Revised: 2 December 2019 / Accepted: 7 December 2019 / Published: 10 December 2019
The purpose of this paper is to rigorously derive the cubic–quintic Ginzburg–Landau equation as a modulation equation for the stochastic Swift–Hohenberg equation with cubic–quintic nonlinearity on an unbounded domain near a change of stability, where a band of dominant pattern is changing stability. Also, we show the influence of degenerate additive noise on the stabilization of the modulation equation. View Full-Text
Keywords: Swift–Hohenberg equation; stabilization by noise; Ginzburg–Landau equation; additive noise; multi-scale analysis Swift–Hohenberg equation; stabilization by noise; Ginzburg–Landau equation; additive noise; multi-scale analysis
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MDPI and ACS Style

Mohammed, W.W. Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line. Mathematics 2019, 7, 1217. https://doi.org/10.3390/math7121217

AMA Style

Mohammed WW. Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line. Mathematics. 2019; 7(12):1217. https://doi.org/10.3390/math7121217

Chicago/Turabian Style

Mohammed, Wael W. 2019. "Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line" Mathematics 7, no. 12: 1217. https://doi.org/10.3390/math7121217

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