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

Wael W. Mohammed
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Wael W. Mohammed: Department of mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2019, vol. 7, issue 12, 1-12

Abstract: 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.

Keywords: Swift–Hohenberg equation; stabilization by noise; Ginzburg–Landau equation; additive noise; multi-scale analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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