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Impact of Multiplicative Noise on Kink Solitons in a Stochastic Higher-Order (2+1)-Dimensional Burgers System |
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PP: 381-399 |
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doi:10.18576/amis/200207
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Author(s) |
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Faisal Muteb K. Almalki,
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Abstract |
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| This study investigates the stochastic higher-order (2+1)-dimensional Burgers equation, a nonlinear partial differential equation that incorporates both higher-order spatial derivatives and multiplicative noise to model complex wave phenomena in dissipative and randomly perturbed environments. Using the singular manifold method and a generalized Cole-Hopf transformation, explicit multi-kink soliton solutions are derived, capturing shock-like profiles and steep-gradient interactions. High-precision numerical simulations validate the analytical solutions and quantify the effects of noise intensity, wave number, and propagation speed. Results show that weak noise largely preserves soliton coherence, whereas stronger stochastic forcing produces pronounced deformations and may trigger instability. Overall, the study elucidates the coupled roles of nonlinearity, dispersion, and randomness, and advances the analysis of stochastic partial differential equations with relevance to fluid dynamics, spintronics, nonlinear optics, and stochastic signal processing. |
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