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

Author

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  • Wael W. Mohammed

    (Department of mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Mathematics Department, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

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.

Suggested Citation

  • Wael W. Mohammed, 2019. "Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line," Mathematics, MDPI, vol. 7(12), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1217-:d:296317
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    Citations

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    Cited by:

    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid," Mathematics, MDPI, vol. 11(10), pages 1-9, May.
    2. Giancarlo Consolo & Gabriele Grifó, 2022. "Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains," Partial Differential Equations and Applications, Springer, vol. 3(5), pages 1-32, October.

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