11 papers
Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations
I. Krichever
The Hamiltonian theory of isomonodromy equations for meromorphic connections with irregular singularities on algebraic curves is constructed. An explicit formula for the symplectic…
Trivalent Graphs and Solitons
I. Krichever, S Novikov
It is shown that the fourth order real self-adjoint difference operator on the Tivalent Tree admits nontrivial deformations preserving one energy level and therefore defines a nont…
Holomorphic bundles and Scalar Difference Operators: One-Point Constructions
I. M. Krichever, S. P. Novikov
Commutative rings of one-dimensional difference operators of rank l>1 and their deformations are effectively constructed. Our analytical constructions are based on the so-called ''…
Periodic and almost periodic potentials in the inverse problems
I. M. Krichever, S. P. Novikov
We review basic ideas and basic examples of the theory of the inverse spectral problems.
Discrete analogs of the Darboux-Egoroff metrics
A. A. Akhmetshin, I. M. Krichever, Y. S. Volvovski
Discrete analogs of the Darboux-Egoroff metrics are considered. It is shown that the corresponding lattices in the Euclidean space are described by discrete analogs of the Lame equ…
The Generating Formula for The Solutions to The Associativity Equations
A. A. Akhmetshin, I. M. Krichever, Y. S. Volvovski
An exact formula for the solutions to the WDVV equation in terms of horizontal sections of the corresponding flat connection is found.