The Analytical Solutions of the Stochastic mKdV Equation via the Mapping Method

Wael W. Mohammed (), Farah M. Al-Askar and Clemente Cesarano
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Wael W. Mohammed: Department of Mathematics, Collage of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Farah M. Al-Askar: Department of Mathematical Science, Collage of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Clemente Cesarano: Section of Mathematics, International Telematic University Uninettuno, Corso, Vittorio, Emanuele II 39, 00186 Roma, Italy

Mathematics, 2022, vol. 10, issue 22, 1-9

Abstract: Here, we analyze the (2+1)-dimensional stochastic modified Kordeweg–de Vries (SmKdV) equation perturbed by multiplicative white noise in the Stratonovich sense. We apply the mapping method to obtain new trigonometric, elliptic, and rational stochastic fractional solutions. Because of the importance of the KdV equation in characterizing the behavior of waves in shallow water, the obtained solutions are beneficial in interpreting certain fascinating physical phenomena. We plot our figures in MATLAB and show several 3D and 2D graphical representations to show how the multiplicative white noise affects the solutions of the SmKdV. We show that the white noise around zero stabilizes SmKdV solutions.

Keywords: stochastic mKdV; the mapping method; exact solutions; stability by noise (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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