Potentials with finite-band spectrum and finite-dimensional reductions of BKM systems (2411.02290v1)

Published 4 Nov 2024 in math-ph, math.DG, math.MP, and nlin.SI

Abstract: We repeat, using methods developed for BKM systems, the famous results of S. Novikov (1974), J. Moser (1981, 1982) , and A. Veselov (1980) that relate Schr\"odinger-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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