Nonlinear Dynamical Analysis and New Solutions of the Space-Fractional Stochastic Davey–Stewartson Equations for Nonlinear Water Waves

Adel Elmandouh, Muneerah Al Nuwairan () and M. M. El-Dessoky
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Adel Elmandouh: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Muneerah Al Nuwairan: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
M. M. El-Dessoky: Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2025, vol. 13, issue 5, 1-17

Abstract: We investigate how novelly generated solutions of the stochastic space-fractional Davey–Stewartson equations are affected by spatial-fractional derivatives and multiplicative Brownian motion (in the Stratonovich sense). These equations model the behavior of weakly nonlinear water waves on a fluid surface. By applying the qualitative theory of planar systems, some new fractional and stochastic solutions are obtained. These solutions gain significance from the application of Davey–Stewartson equations to the theory of turbulence for plasma waves, as they can explain several fascinating physical phenomena. Some solutions are graphically displayed to illustrate the influence of noise strength and fractional derivatives on the obtained solutions. These effects influence the solution’s amplitude and width, as well as its smoothness.

Keywords: bifurcation theory; wave solutions; modified Riemann–Liouville derivative; stochastic fractional differential equations; nonlinear water waves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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