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Dynamics of Kink and Multi-Kink Solitons in the Stochastic (2+1)-Dimensional Burgers Equation with Multiplicative White Noise |
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PP: 1481-1499 |
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doi:10.18576/amis/190619
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Author(s) |
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Ibtisam Daqqa,
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Abstract |
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| This paper investigates the stochastic (2+1)-dimensional Burgers equation, a fundamental nonlinear partial differential equation (PDE) widely used to model shock formation, soliton propagation, and complex spatiotemporal dynamics. The stochastic formulation incorporates multiplicative noise, allowing for the analysis of systems subject to random fluctuations and environmental disturbances. First, the equation is reformulated using a wave transformation technique to establish a unified analytical framework. Explicit solutions of the deterministic counterpart are then derived through two complementary approaches: the Singular manifold method and the multiple-kink wave solution technique. These solutions form the foundation for studying the impact of noise and parameter variations on soliton stability and morphology. Comprehensive numerical simulations are performed to evaluate the evolution of kink and multi-kink solitons under varying noise intensities and initial conditions. The results demonstrate that while solitons preserve their core structural features under weak stochastic perturbations, increased noise intensity leads to significant amplitude distortions, phase fluctuations, and, in some cases, loss of coherence. These findings highlight the dual role of multiplicative noise, which can induce minor modulations at low levels but severely disrupt nonlinear balance at higher intensities. This work fills a critical research gap by systematically examining the stochastic (2+1)-dimensional Burgers equation and provides insights relevant to practical applications in physics and engineering, particularly in areas where soliton stability in noisy environments is essential. |
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