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<p>This study for the first time addresses the exact solution problem of the cubic-quintic-septic Biswas-Milovic equation under multiplicative white noise perturbation, breaking through the limitation of traditional methods relying on preassumed solution forms. By leveraging the polynomial complete discriminant system and systematic parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation> optimization, we eliminate noise interference and derive 12 categories of exact solutions with non-predefined structures, including trigonometric, solitary wave, and implicit function solutions. Key theoretical findings reveal that non-averaged solutions strictly preserve soliton characteristics, while stochastic averaging is disrupted by delay factors—this mechanism establishes new criteria for noise-resistant soliton design. This research not only constructs a rigorous analytical theory for stochastic high-order Biswas-Milovic equation but also provides noise-resistant optimization metrics for optical communication systems, enabling a direct mapping from mathematical theorems to fiber parameter design.</p>

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Exact solutions and stochastic averaging of the cubic-quintic-septic Biswas-Milovic equation under multiplicative white noise perturbation

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • Shirong Liu

摘要

This study for the first time addresses the exact solution problem of the cubic-quintic-septic Biswas-Milovic equation under multiplicative white noise perturbation, breaking through the limitation of traditional methods relying on preassumed solution forms. By leveraging the polynomial complete discriminant system and systematic parameter \(n\) optimization, we eliminate noise interference and derive 12 categories of exact solutions with non-predefined structures, including trigonometric, solitary wave, and implicit function solutions. Key theoretical findings reveal that non-averaged solutions strictly preserve soliton characteristics, while stochastic averaging is disrupted by delay factors—this mechanism establishes new criteria for noise-resistant soliton design. This research not only constructs a rigorous analytical theory for stochastic high-order Biswas-Milovic equation but also provides noise-resistant optimization metrics for optical communication systems, enabling a direct mapping from mathematical theorems to fiber parameter design.