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<p>In this article, we execute the hirota method with bilinearization on the generalized Bogoyavlensky-Konopelchenko equation to obtain the new three wave, lump-kink wave and rogue wave solitons of the consider equation and execute the Multi-Layer-Perceptron Regressor machine learning algorithm to predict the behavior of the solitons. Also, we discuss the integrability of the considered generalized Bogoyavlensky-Konopelchenko equation through the Painleve analysis that shows the given equation is integrable and fulfills the criteria of the Painleve analysis and this equation can be used in future work. The obtained new three wave, lump-kink wave and rogue wave solitons are new and more reliable.The acquired solitons also confirmed through the mathematical software. The comparison of solitons with the actual and predicted results disclosed in the paper shows that our gained solitons are more reliable and authentic. Modulation instability apply on the given equation and verify through the MLP regressor algorithm. Some of the gained outcomes are illustrated by 2D, 3D and contour surfaces and the using neural network algorithm to predict results in the 2D plot of physical behavior of the our actual solutions and losses with tables.</p>

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Bilinearization of generalized Bogoyavlensky-Konopelchenko equation for Solitons with Neural Network: Painleve analysis

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Waseem Razzaq,
  • Asim Zafar

摘要

In this article, we execute the hirota method with bilinearization on the generalized Bogoyavlensky-Konopelchenko equation to obtain the new three wave, lump-kink wave and rogue wave solitons of the consider equation and execute the Multi-Layer-Perceptron Regressor machine learning algorithm to predict the behavior of the solitons. Also, we discuss the integrability of the considered generalized Bogoyavlensky-Konopelchenko equation through the Painleve analysis that shows the given equation is integrable and fulfills the criteria of the Painleve analysis and this equation can be used in future work. The obtained new three wave, lump-kink wave and rogue wave solitons are new and more reliable.The acquired solitons also confirmed through the mathematical software. The comparison of solitons with the actual and predicted results disclosed in the paper shows that our gained solitons are more reliable and authentic. Modulation instability apply on the given equation and verify through the MLP regressor algorithm. Some of the gained outcomes are illustrated by 2D, 3D and contour surfaces and the using neural network algorithm to predict results in the 2D plot of physical behavior of the our actual solutions and losses with tables.