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Abstract <p> We establish a rigorous Riemann–Hilbert (RH) framework for the coupled modified Yajima–Oikawa system. Unlike conventional approaches that initiate spectral analysis with the spatial Lax operator, we employ its temporal counterpart to derive the requisite analytic spectral functions and thereby formulate the associated RH problem. We then obtain explicit multi-soliton solutions in the reflectionless case. Leveraging symbolic computations in Maple, we analyze the ensuing soliton dynamics and illustrate their interactions. Our RH methodology not only elucidates the intricate spectral features of the coupled modified Yajima–Oikawa system but also provides a systematic procedure for constructing its general <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N\)</EquationSource> </InlineEquation>-soliton solutions. </p>

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The \(N\)-soliton solutions for coupled modified Yajima–Oikawa system via the Riemann–Hilbert method

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Tanlin Li,
  • Yuxuan Li,
  • Lin Huang

摘要

Abstract

We establish a rigorous Riemann–Hilbert (RH) framework for the coupled modified Yajima–Oikawa system. Unlike conventional approaches that initiate spectral analysis with the spatial Lax operator, we employ its temporal counterpart to derive the requisite analytic spectral functions and thereby formulate the associated RH problem. We then obtain explicit multi-soliton solutions in the reflectionless case. Leveraging symbolic computations in Maple, we analyze the ensuing soliton dynamics and illustrate their interactions. Our RH methodology not only elucidates the intricate spectral features of the coupled modified Yajima–Oikawa system but also provides a systematic procedure for constructing its general \(N\) -soliton solutions.