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math-ph2004
Symmetries and Lagrangian time-discretizations of Euler equations
Alexei V. Penskoi
In the late 80s - early 90s J. Moser and A. P. Veselov considered Lagrangian discrete systems on Lie groups with additional symmetry conditions imposed on Lagrangians. They observe…
math-ph2003
Laplace transformations and spectral theory of two-dimensional semi-discrete and discrete hyperbolic Schroedinger operators
Alexei A. Oblomkov, Alexei V. Penskoi
We introduce Laplace transformations of 2D semi-discrete hyperbolic Schroedinger operators and show their relation to a semi-discrete 2D Toda lattice. We develop the algebro-geomet…
math-ph2003
Discrete matrix Riccati equations with superposition formulas
Alexei V. Penskoi, Pavel Winternitz
An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinea…