论文信息 - From Bi-Hamiltonian Geometry to Separation of Variables: Stationary Harry-Dym and the KdV Dressing Chain

From Bi-Hamiltonian Geometry to Separation of Variables: Stationary Harry-Dym and the KdV Dressing Chain

Abstract Separability theory of one-Casimir Poisson pencils, written down in arbitrary coordinates, is presented. Separation of variables for stationary Harry-Dym and the KdV dressing chain illustrates the theory.

Maciej Blaszak | M. Błaszak

[1] D. Mumford. Tata Lectures on Theta I , 1982 .

[2] Inverse bi-Hamiltonian separable chains , 2000 .

[3] I. Gelfand,et al. On the Local Geometry of a Bihamiltonian Structure , 1993 .

[4] O. Babelon,et al. Hamiltonian structures and Lax equations , 1990 .

[5] Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy , 1999, solv-int/9906009.

[6] M. Błaszak. Degenerate Poisson Pencils on Curves: New Separability Theory , 2000, nlin/0004002.

[7] E. Sklyanin,et al. Separation of variables , 2004, Mathematical Methods of Theoretical Physics.

[8] Maciej Błaszak,et al. Multi-Hamiltonian Theory of Dynamical Systems , 1998 .

[9] Two newton decompositions of staionary flows of KdV and Harry Dym hierarchies , 1996 .

[10] A. Shabat. The infinite-dimensional dressing dynamical system , 1992 .