On the peakon solutions of some stochastic nonlinear evolution equations


Yokus A., Taşkesen H., Alaloush M., Demirdag B.

OPTICAL AND QUANTUM ELECTRONICS, vol.53, no.10, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 10
  • Publication Date: 2021
  • Doi Number: 10.1007/s11082-021-03240-z
  • Title of Journal : OPTICAL AND QUANTUM ELECTRONICS
  • Keywords: Stochastic Camassa-Holm type equation, Stochastic Fornberg-Whitham equation, Exact solution, Noise, (1/G ')-expansion, CAMASSA-HOLM EQUATION, GLOBAL CONSERVATIVE SOLUTIONS, TRAVELING-WAVE SOLUTIONS, SHALLOW-WATER EQUATION, WELL-POSEDNESS

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.