English

On the Dubrovin Equations for the Finite-gap Potentials

Exactly Solvable and Integrable Systems 2007-05-23 v2 Pattern Formation and Solitons

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.

Keywords

Cite

@article{arxiv.nlin/0106024,
  title  = {On the Dubrovin Equations for the Finite-gap Potentials},
  author = {Yurii V. Brezhnev},
  journal= {arXiv preprint arXiv:nlin/0106024},
  year   = {2007}
}

Comments

4 pages, no figures