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On the peakon solutions of some stochastic nonlinear evolution equations

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Abstract

In this paper, stochastic Fornberg–Whitham and a stochastic Camassa–Holm (CH) type equations are studied. A Galilean transformation which previously used for a stochastic KdV equation is employed to transform the equations into their deterministic counterparts. Then \((1/G')\)-expansion method is used to obtain analytical solutions. 2D, 3D, and contour graphs representing the peakon solutions have been plotted by assigning special values to the constants in the solutions via computer software. In addition, by giving different random values to the external noise, the effect of the noise on the wave-forms has been exhibited. The obtained results have been discussed in detail.

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Funding

The second and third authors are supported by the Research Fund of Van Yuzuncu Yil University [grant number FDK-2020-8881].

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Authors and Affiliations

  1. Department of Mathematics, Firat University, 23200, Elazig, Turkey

    Asıf Yokuş

  2. Department of Mathematics, Van Yuzuncu Yil University, 65080, Van, Turkey

    Hatice Taskesen

  3. Department of Statistics, Van Yuzuncu Yil University, 65080, Van, Turkey

    Mohanad Alaloush

  4. Department of Actuary, Hacettepe University, 06800, Ankara, Turkey

    Betül Deniz Demirdaǧ

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  1. Asıf Yokuş
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  2. Hatice Taskesen
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  3. Mohanad Alaloush
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  4. Betül Deniz Demirdaǧ
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Correspondence to Asıf Yokuş.

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Yokuş, A., Taskesen, H., Alaloush, M. et al. On the peakon solutions of some stochastic nonlinear evolution equations. Opt Quant Electron 53, 586 (2021). https://doi.org/10.1007/s11082-021-03240-z

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