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<p>This study is dedicated to an in-depth exploration of the integrable structure inherent in the coupled KdV equation, with particular emphasis on solving Lax pairs and their application in constructing Darboux Transformation and Bäcklund Transformation. By leveraging these transformations, we have derived a series of superposition formulas that offer novel insights into understanding the interactions among solitary waves within coupled systems. Furthermore, our successful identification of a recursive operator for this system not only enhances our comprehension of the dynamical behaviors exhibited by the coupled KdV equations but also establishes a theoretical cornerstone for future research endeavors in this field.</p>

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Darboux Transformations of Nonlinear Coupled Equations and Their Solutions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月16日

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  • Jihong Wang,
  • Lixiu Wang,
  • Jia Yangjie

摘要

This study is dedicated to an in-depth exploration of the integrable structure inherent in the coupled KdV equation, with particular emphasis on solving Lax pairs and their application in constructing Darboux Transformation and Bäcklund Transformation. By leveraging these transformations, we have derived a series of superposition formulas that offer novel insights into understanding the interactions among solitary waves within coupled systems. Furthermore, our successful identification of a recursive operator for this system not only enhances our comprehension of the dynamical behaviors exhibited by the coupled KdV equations but also establishes a theoretical cornerstone for future research endeavors in this field.