The generalized periodic ultradiscrete KdV equation and its background solutions

We investigate the ultradiscrete KdV equation with periodic boundary conditions where the two parameters (capacity of the boxes and that of the carrier) are arbitrary integers. We give a criterion to allow a periodic boundary condition when initial states take arbitrary integer values. Conserved quantities are constructed for the periodic systems. Construction of background solutions of the periodic ultradiscrete KdV equation from the Jacobi theta function is also presented.Comment: 20 pages, 7 figures, v2: final form to appear in J. Math. Sci. Univ. Toky

Integrability of Discrete Equations Modulo a Prime

We apply the 'almost good reduction' (AGR) criterion, which has been introduced in our previous (arXiv:1206.4456 and arXiv:1209.0223), to several classes of discrete integrable equations. We verify our conjecture that AGR plays the same role for maps of the plane define over simple finite fields as the notion of the singularity confinement does. We first prove that q-discrete analogues of the Painlev\'e III and IV equations have AGR. We next prove that the Hietarinta-Viallet equation, a non-integrable chaotic system also has AGR

Numerical Study of Two-fluid Flowing Equilibria of Helicity-driven Spherical Torus Plasmas

Two-fluid flowing equilibrium configurations of a helicity-driven spherical torus (HD-ST) are numerically determined by using the combination of the finite difference and the boundary element methods. It is found from the numerical results that electron fluids near the central conductor are tied to an external toroidal field and ion fluids are not. The magnetic configurations change from the high-$q$ HD-ST ($q$>1) with paramagnetic toroidal field and low-$\beta$ (volume average $\beta$ value, ($\approx$ 2 %) through the helicity-driven spheromak and RFP to the ultra low-$q$ HD-ST (0<q<1) with diagmagnetic toroidal field and high-$\beta$ ($\beta\approx 18\%) as the external toroidal field at the inner edge region decreases and reverses the sign. The two-fluid effecs are more significant in this equilibrium transition when the ion diagmagnetic drift is dominant in the flowing two-fluid.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France