• Corpus ID: 203610385

Matrix KP hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy

@article{Prokofev2019MatrixKH,
  title={Matrix KP hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy},
  author={V. Prokofev and A. Zabrodin},
  journal={arXiv: Mathematical Physics},
  year={2019}
}
We consider solutions of the matrix KP hierarchy that are trigonometric functions of the first hierarchical time $t_1=x$ and establish the correspondence with the spin generalization of the trigonometric Calogero-Moser system on the level of hierarchies. Namely, the evolution of poles $x_i$ and matrix residues at the poles $a_i^{\alpha}b_i^{\beta}$ of the solutions with respect to the $k$-th hierarchical time of the matrix KP hierarchy is shown to be given by the Hamiltonian flow with the… 

Elliptic solutions to matrix KP hierarchy and spin generalization of elliptic Calogero–Moser model

We consider solutions of the matrix KP hierarchy that are elliptic functions of the first hierarchical time t1 = x. It is known that poles xi and matrix residues at the poles ρ i = a α i b β i of

References

SHOWING 1-10 OF 27 REFERENCES

KP hierarchy and trigonometric Calogero–Moser hierarchy

We consider trigonometric solutions of the KP hierarchy. It is known that their poles move as particles of the Calogero-Moser model with trigonometric potential. We show that this correspondence can

Integrable time-discretisation of the Ruijsenaars-Schneider model

An exactly integrable symplectic correspondence is derived which in a continuum limit leads to the equations of motion of the relativistic generalization of the Calogero-Moser system, that was

KP Trigonometric Solitons and an Adelic Flag Manifold

We show that the trigonometric solitons of the KP hierarchy enjoy a differential- difference bispectral property, which becomes transparent when translated on two suitable spaces of pairs of matrices

The n-Component KP Hierarchy and Representation Theory

It is the aim of the present article to give all formulations of the n-component KP hierarchy and clarify connections between them. The generalization to the n-component KP hierarchy is important

Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy

  • A. Zabrodin
  • Mathematics
    Journal of Mathematical Physics
  • 2019
We introduce the discrete time version of the spin Calogero-Moser system. The equations of motion follow from the dynamics of poles of rational solutions to the matrix KP hierarchy with discrete

Elliptic Solutions to Difference Non-Linear Equations and Related Many-Body Problems

Abstract:We study algebro-geometric (finite-gap) and elliptic solutions of fully discretized KP or 2D Toda equations. In bilinear form they are Hirota's difference equation for τ-functions. Starting

A time-discretized version of the Calogero-Moser model

Integrable hierarchies and dispersionless limit

Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical

A generalisation of the Calogero-Moser system