This work investigates the stochastic dynamics of the nonlinear Maccari system by incorporating Brownian motion into its evolution equations, modeling random fluctuations relevant to physical settings such as optical fibers, plasma waves, and fluid interfaces, where noise significantly influences wave propagation. To obtain solitary wave solutions under stochastic effects, we use the refined Riccati–Bernoulli subsidiary ordinary differential equation (RB sub-ODE) method to reduce the stochastic partial differential equations (PDEs) to a manageable system of ordinary differential equations. This methodology enables the construction of a diverse family of stochastic wave solutions, including rational profiles, periodic structures, and solitary waves with noise-dependent modulation. The obtained solutions reveal significant influences of stochastic forcing on amplitude, phase, stability, and interaction dynamics. The results demonstrate that even weak noise can induce substantial modulation, phase drift, and deformation of coherent structures in the Maccari system. To illustrate the propagation of solitary waves for the stochastic nonlinear Maccari system, 2D charts of selected solutions are created using Matlab. Overall, this work offers a robust framework for analyzing noise-driven wave phenomena and highlights the effectiveness of the RB sub-ODE technique in deriving exact stochastic solutions for complex integrable models.
Citation: Theyab Alrashdi. Noise-induced modulation of solitary waves in the nonlinear Maccari system[J]. AIMS Mathematics, 2026, 11(2): 4465-4478. doi: 10.3934/math.2026179
This work investigates the stochastic dynamics of the nonlinear Maccari system by incorporating Brownian motion into its evolution equations, modeling random fluctuations relevant to physical settings such as optical fibers, plasma waves, and fluid interfaces, where noise significantly influences wave propagation. To obtain solitary wave solutions under stochastic effects, we use the refined Riccati–Bernoulli subsidiary ordinary differential equation (RB sub-ODE) method to reduce the stochastic partial differential equations (PDEs) to a manageable system of ordinary differential equations. This methodology enables the construction of a diverse family of stochastic wave solutions, including rational profiles, periodic structures, and solitary waves with noise-dependent modulation. The obtained solutions reveal significant influences of stochastic forcing on amplitude, phase, stability, and interaction dynamics. The results demonstrate that even weak noise can induce substantial modulation, phase drift, and deformation of coherent structures in the Maccari system. To illustrate the propagation of solitary waves for the stochastic nonlinear Maccari system, 2D charts of selected solutions are created using Matlab. Overall, this work offers a robust framework for analyzing noise-driven wave phenomena and highlights the effectiveness of the RB sub-ODE technique in deriving exact stochastic solutions for complex integrable models.
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Theyab Alrashdi. Noise-induced modulation of solitary waves in the nonlinear Maccari system[J]. AIMS Mathematics, 2026, 11(2): 4465-4478. doi: 10.3934/math.2026179
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