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We repeat, using methods developed for BKM systems, the famous results of S. Novikov [45], J. Moser [41, 42], and A. Veselov [50] that relate Schrödinger-Hill operators with finite-band spectra, solutions of the Neumann system, and certain solutions of the KdV equations. Our general motivation is to determine whether it is possible to apply inverse scattering methods to BKM systems, and in the conclusion, we indicate initial observations in this direction.

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Thoughts about potentials with finite-band spectrum and finite-dimensional reductions of integrable systems

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  • 发表日期：

    2026年

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  • Andrey Yu. Konyaev,
  • Vladimir S. Matveev

摘要

We repeat, using methods developed for BKM systems, the famous results of S. Novikov [45], J. Moser [41, 42], and A. Veselov [50] that relate Schrödinger-Hill operators with finite-band spectra, solutions of the Neumann system, and certain solutions of the KdV equations. Our general motivation is to determine whether it is possible to apply inverse scattering methods to BKM systems, and in the conclusion, we indicate initial observations in this direction.