Next Article in Journal
Periodic Solutions for a Four-Dimensional Coupled Polynomial System with N-Degree Homogeneous Nonlinearities
Previous Article in Journal
A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type
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
Show Figures

Figure 1

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop