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<p>We investigate in the present work the spectral stability of elliptic function solutions for the AB system, a completely integrable model for the description of baroclinic waves in geophysical flow. With the aid of the algebraic geometry method, we derive the elliptic solutions of the AB system and its corresponding solutions of the Lax pair which are represented by theta functions. By establishing the squared-eigenfunction connection between the non-standard linear stability problem and the Lax spectral problem, we prove that the elliptic solutions are spectrally stable with respect to subharmonic perturbations.</p>

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Spectral Stability of Elliptic Solutions for the AB System

  • 期刊论文

  • 发表日期：

    2025年8月23日

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  • Li-Ming Cao,
  • Shou-Fu Tian

摘要

We investigate in the present work the spectral stability of elliptic function solutions for the AB system, a completely integrable model for the description of baroclinic waves in geophysical flow. With the aid of the algebraic geometry method, we derive the elliptic solutions of the AB system and its corresponding solutions of the Lax pair which are represented by theta functions. By establishing the squared-eigenfunction connection between the non-standard linear stability problem and the Lax spectral problem, we prove that the elliptic solutions are spectrally stable with respect to subharmonic perturbations.