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).

Moduli stacks of polarized K3 surfaces in mixed characteristic

2000 Mathematics Subject Classification: 14J28, 14D22.

Generalizations of Cole's Systems

There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.

Perturbations of Systems Describing the Motion of a Particle in Central Fields

The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.

Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75