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Numerical realizations of solutions of the stochastic KdV equation

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  • Herman, Russell L.
  • Rose, Andrew

Abstract

We investigate simulations of exact solutions of the stochastic Korteweg–deVries equation under additive noise. We compare the expectation values of the exact solutions to theoretical expectation values and to the numerical simulations of the stochastic Korteweg–deVries equation with and without damping. We find on average the diffused soliton vanishes long before the typically reported asymptotic limit.

Suggested Citation

  • Herman, Russell L. & Rose, Andrew, 2009. "Numerical realizations of solutions of the stochastic KdV equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 164-172.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:1:p:164-172
    DOI: 10.1016/j.matcom.2009.06.008
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    Cited by:

    1. Yuan, Rui-rui & Shi, Ying & Zhao, Song-lin & Wang, Wen-zhuo, 2024. "The mKdV equation under the Gaussian white noise and Wiener process: Darboux transformation and stochastic soliton solutions," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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