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Stochastic Effects on Soliton Dynamics in the KdV Equation with Multiplicative White Noise |
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PP: 1369-1382 |
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doi:10.18576/amis/190611
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Author(s) |
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Hanadi M. Adel-Salam,
Faisal Muteb K. Almalki,
Ibtisam Daqqa,
Mortada S. Ali,
Halla Elemam,
Abdelgalal Abaker,
Emad A-B Abdel-Salam,
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Abstract |
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| This research seeks to investigate the impact of multiplicative white noise on the dynamical properties of soliton solutions (SS) within the outline of the KdV equation. While conventional KdV models describe nonlinear wave propagation in deterministic settings, real-world systems are frequently subjected to stochastic disturbances that can notably alter wave dynamics. By incorporating multiplicative white noise, this study examines the effects of random variations on soliton stability, morphology, and propagation. The Adomian decomposition and the simplest equation techniques are utilized to obtain solitary and SS, which are further validated through numerical simulations. This methodology enables the exploration of stochastic influences on soliton interactions and their long-term evolution. The results suggest that noise induces soliton deformation, amplitude modulation, and potential loss of coherence, underscoring the significant role of stochastic processes in nonlinear wave behavior. The findings highlight the resilience of solitons in the presence of random perturbations, providing valuable insights for applications in fields such as fluid dynamics, optical fiber communications and plasma physics. Additionally, the study discusses the interaction between two solitons using the superposition method. |
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