On the Dubrovin Equations for the Finite-gap Potentials

Details On the Dubrovin Equations for the Finite-gap Potentials On the Dubrovin Equations for the Finite-gap Potentials

2001-06-15

arxiv.org/abs/nlin/0106024v2

Russ. Math. Surveys (2002), v.57(2), 415-417. Uspekhi Mat. Nauk (2002), 57(1), 191-192 (in Russian)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

4 pages, no figures

Scientific paper

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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