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<p>We show that the equations of motion of a rigid body about a fixed point in the Newtonianfield with a quadratic potential are special reduction of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. Some new explicit solutions of the corresponding matrix system and the spectral properties of the related Schrödinger operators are discussed.</p>

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Spinning Top in Quadratic Potential and Matrix Dressing Chain

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Vsevolod E. Adler,
  • Alexander P. Veselov

摘要

We show that the equations of motion of a rigid body about a fixed point in the Newtonianfield with a quadratic potential are special reduction of period-one closure of the Darboux dressing chain for the Schrödinger operators with matrix potentials. Some new explicit solutions of the corresponding matrix system and the spectral properties of the related Schrödinger operators are discussed.