2,157 research outputs found
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- HD-ST (>1) with paramagnetic toroidal field and low-
(volume average value, ( 2 %) through the
helicity-driven spheromak and RFP to the ultra low- HD-ST (0<q<1) with
diagmagnetic toroidal field and high- ($\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
- …