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On the Dubrovin Equations for the Finite-gap Potentials

Yurii V. Brezhnev
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Abstract

The general technique of derivation of Dubrovin's equation for the arbitrary operator pencils is suggested. The question of unique recovering of the finite-gap potential by coordinates of zeroes of the Psi-function is discussed. The crucial result of the paper is an autonomous form of Dubrovin's equations and new trace-formulas for nontrivial spectral problems of the 3-rd order with trigonal algebraic curve. We show only demonstrative examples, the method is spread into arbitrary spectral problem including matrix ones.

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Yurii V. Brezhnev. 2001-06-21. On the Dubrovin Equations for the Finite-gap Potentials. https://arxiv.org/abs/nlin/0106024

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