3 papers
nlin.SI2005
Historical remarks to finite-gap integration theory: elementary treatment of the theory
Yu. V. Brezhnev
In the example of the Schrödinger/KdV equation we give elementary treatment of the theory of finite-gap integration. The concept is equivalent to two kinds of Liouvillian integrabi…
nlin.SI2001
On the Dubrovin Equations for the Finite-gap Potentials
Yurii V. Brezhnev
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 coordin…
nlin.SI2000
On Psi-function for finite-gap potentials
N. V. Ustinov, Yu. V. Brezhnev
A way to derive an explicit formulae in terms of the potentials, if they are finite-gap, for the solutions of spectral problems and corresponding algebraic curves is presented.