Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line
Abstract
:1. Introduction
2. Space and Mild Solution
3. Derivation of Cubic–Quintic Ginzburg–Landau Equation
4. General Bounds on OU Process
5. Main Results
6. The Effect of Degenerate Additive Noise
- The coefficient of the cubic term is positive for and is a non-positive otherwise,
- The coefficient of the linear term is positive for if or if and is a non-positive otherwise.
7. Conclusions
Funding
Acknowledgments
Conflicts of Interest
References
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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
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 StyleMohammed, 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
APA StyleMohammed, W. W. (2019). Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line. Mathematics, 7(12), 1217. https://doi.org/10.3390/math7121217