arXiv subjects

A. Akhmetshin

Publications and source records attributed to A. Akhmetshin.

3 recordsLinked to original sources

arXiv2002

Elliptic Families of Solutions of the Kadomtsev-Petviashvili Equation and the Field Elliptic Calogero-Moser System

We present the Lax pair for the field elliptic Calogero-Moser system and establish a connection between this system and the Kadomtsev-Petviashvili equation. Namely, we consider elliptic families of solutions of the KP equation, such that their poles satisfy a constraint of being balanced. We show that the dynamics of these poles is described by a reduction of the field elliptic CM system. We construct a wide class of solutions to the field elliptic CM system by showing that any N-fold branched cover of an elliptic curve gives rise to an elliptic family of solutions of the KP equation with balanced poles.

hep-th↗

arXiv2000

The dynamics of zeros of the finite-gap solutions to the Schrodinger equation

Following the recent paper by J. F. van Diejen and H. Puschmann we investigate the behavior of zeros of the finite-gap solutions to the Schrodinger equation. As a result, a new system of particles on a punctured Riemann surface is constructed. It is shown to be Hamiltonian and integrable.

hep-th↗

arXiv2000

The dynamics of zeros of the elliptic solutions to the Schrodinger equation

J. F. van Diejen and H. Puschmann have recently shown that the dynamics of zeros of the n-solitonic solutions to the Schrodinger equation with the reflectionless potential is governed by a rational Ruijsenaars-Schneider system. We use the algebraic-geometrical construction of solutions to the Schrodinger equation to generalize this result to the elliptic case.

hep-th↗