Stefan Wojciechowski

TL;DR: In this paper, a Miura map between the finite dimensional phase spaces of stationary flows of integrable nonlinear evolution equations is presented, which is used to construct a finite bi-hamiltonian ladder for such systems.

TL;DR: In this article, it was shown that the Henon-heiles hamiltonian H = 1 2 (x 2 + y 2 + ω 1 x 2+ ω 2 y 2 ) + a(x 2 y + 2y 3 ) is separable in shifted parabolic coordinates and the solution of the Hamilton-Jacobi equation is expressible in terms of hyperelliptic integrals.

TL;DR: In this article, the integrability of the Calogero-Moser system in an external quartic potential is proved and the Backlund transformation for this system is found.

TL;DR: A Backlund transformation for a generalised Calogero-Moser system, in which the particles posses extra, internal, degrees of freedom, is given in this paper, which is shown to be a canonical transformation and its generating function is given explicitly.

TL;DR: In this paper, the authors introduced and solved a completely integrable N -body system in one dimension, which is degenerate in the sense that it has 2 N − 1 independent integrals of motion which determine its trajectories uniquely.