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<p>Rogue wave is a localized wave that exists in many nonlinear integrable systems. In this paper, the <i>N</i>-order rogue wave solutions of the Benjamin-Ono (BO) equation are figured out with the aid of the Kadomtsev-Petviashvili (KP) hierarchy reduction method based on the Hirota bilinear framework. Further, by employing asymptotic analysis techniques, the distribution patterns of rogue waves in the BO equation are predicted quantitatively through the zeros of Yablonskii-Vorob’ev (YV) polynomials and Adler-Moser (AM) polynomials. These patterns perfectly align with the exact solutions. Additionally, a general modulation instability (MI) analysis of the BO equation is carried out.</p>

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On the Role of AM Polynomial Roots in the Determination of Rogue Wave Patterns in Benjamin-ono Equation

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Fuzhuang Zheng,
  • Zhenyun Qin,
  • Gui Mu,
  • Tingyou Wang

摘要

Rogue wave is a localized wave that exists in many nonlinear integrable systems. In this paper, the N-order rogue wave solutions of the Benjamin-Ono (BO) equation are figured out with the aid of the Kadomtsev-Petviashvili (KP) hierarchy reduction method based on the Hirota bilinear framework. Further, by employing asymptotic analysis techniques, the distribution patterns of rogue waves in the BO equation are predicted quantitatively through the zeros of Yablonskii-Vorob’ev (YV) polynomials and Adler-Moser (AM) polynomials. These patterns perfectly align with the exact solutions. Additionally, a general modulation instability (MI) analysis of the BO equation is carried out.