Solitary Wave Solutions for the Stochastic Fractional-Space KdV in the Sense of the M-Truncated Derivative

Wael W. Mohammed (), Clemente Cesarano, Farah M. Al-Askar and Mahmoud El-Morshedy
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Wael W. Mohammed: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Clemente Cesarano: Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Farah M. Al-Askar: Department of Mathematical Science, Collage of Science, Princess Nourah Bint, Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mahmoud El-Morshedy: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Mathematics, 2022, vol. 10, issue 24, 1-11

Abstract: The stochastic fractional-space Korteweg–de Vries equation (SFSKdVE) in the sense of the M-truncated derivative is examined in this article. In the Itô sense, the SFSKdVE is forced by multiplicative white noise. To produce new trigonometric, hyperbolic, rational, and elliptic stochastic fractional solutions, the tanh–coth and Jacobi elliptic function methods are used. The obtained solutions are useful in interpreting certain fascinating physical phenomena because the KdV equation is essential for understanding the behavior of waves in shallow water. To demonstrate how the multiplicative noise and the M-truncated derivative impact the precise solutions of the SFSKdVE, different 3D and 2D graphical representations are plotted.

Keywords: stochastic KdV; fractional KdV; analytical solutions; stability by noise (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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