Poincaré integral invariant and conserved quantity of Toda lattice systems

抄録

Numerical properties of the Poincaré integral invariant of the Toda lattice systems are investigated based on the discrete Fourier interpolation method. In the 1D Toda lattice, we show that the Poincaré integral invariant is conserved in a finite time interval in a symplectic time integration. In contrast, a conserved quantity of the 2D Toda lattice is conserved for a long time interval because of the interaction perpendicular to the lattice direction.