Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Supersymmetry and Ghosts in Quantum Mechanics

2000 Mathematics Subject Classification: 81Q60, 35Q40.