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<p>The Riemann-Hilbert (RH) approach is applied to the generalized Chen-Lee-Liu (GCLL) equation. By establishing the analytical, asymptotic, and symmetrical properties of the Lax pair and the Jost solution associated with this equation, we construct a modified RH problem that adheres to the normalization conditions. Building upon this foundation, we utilize the Cauchy-Binet formula to present for the first time an explicit determinant representation of the multi-soliton solution for this equation. Furthermore, we derive specific expressions for both first-order and second-order solitons. Through a comprehensive asymptotic analysis of multi-soliton collisions, we rigorously demonstrate that these collisions are elastic and provide explicit formulas for both spatial displacement and phase shift of each soliton. This methodology is not only applicable to the GCLL equation but also offers a systematic RH framework for addressing integrable systems characterized by non-standard spectral features.</p>

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The Riemann–Hilbert Approach to Explicit Multi-Solitons and Collisions for the Generalized Chen–Lee–Liu Equation

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Wenxia Chen,
  • Yu Dou,
  • Chaosheng Zhang,
  • Lixin Tian

摘要

The Riemann-Hilbert (RH) approach is applied to the generalized Chen-Lee-Liu (GCLL) equation. By establishing the analytical, asymptotic, and symmetrical properties of the Lax pair and the Jost solution associated with this equation, we construct a modified RH problem that adheres to the normalization conditions. Building upon this foundation, we utilize the Cauchy-Binet formula to present for the first time an explicit determinant representation of the multi-soliton solution for this equation. Furthermore, we derive specific expressions for both first-order and second-order solitons. Through a comprehensive asymptotic analysis of multi-soliton collisions, we rigorously demonstrate that these collisions are elastic and provide explicit formulas for both spatial displacement and phase shift of each soliton. This methodology is not only applicable to the GCLL equation but also offers a systematic RH framework for addressing integrable systems characterized by non-standard spectral features.