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Using the techniques of inverse balancing and AI-assisted generalized differential operator method, deformed kink solitary solutions to a non-autonomous Riccati system with diffusive coupling are derived. Such solutions are a generalization of kink solitary solutions within the classical solitary solution architecture: while the classical solitary solutions use an exponential time transformation, deformed solitary may have any non-singular transformation function. The construction of such solutions is a multi-stage process, requiring the solution of a specific system of nonlinear equations with respect to the system and solution parameters. An AI-based tool is applied to investigate the symbolic big data set to prune a large number of degenerate cases, greatly increasing the efficiency of the presented approach.

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Deformed Solitary Solutions to Nonlinear Differential Equations Based on the AI-Assisted Generalized Operator of Differentiation

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  • 发表日期：

    2025年

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  • Zenonas Navickas,
  • Romas Marcinkevicius,
  • Inga Telksniene,
  • Tadas Telksnys,
  • Minvydas Ragulskis

摘要

Using the techniques of inverse balancing and AI-assisted generalized differential operator method, deformed kink solitary solutions to a non-autonomous Riccati system with diffusive coupling are derived. Such solutions are a generalization of kink solitary solutions within the classical solitary solution architecture: while the classical solitary solutions use an exponential time transformation, deformed solitary may have any non-singular transformation function. The construction of such solutions is a multi-stage process, requiring the solution of a specific system of nonlinear equations with respect to the system and solution parameters. An AI-based tool is applied to investigate the symbolic big data set to prune a large number of degenerate cases, greatly increasing the efficiency of the presented approach.