| Abstract: |
| We introduce a class of recursions defined over the $d$-dimensional integer lattice.
The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation and the discrete KdV equation.
These equations have polynomial forms which can be regarded as extensions of the bilinear forms of the integrable equations, and their $\tau$ function analogues show the Laurent phenomena.
We shall prove that the equations satisfy the coprimeness property, which is one of integrability detectors analogous to the singularity confinement test.
In spite of the fact that the degree of their iterates grows exponentially, they exhibit pseudo-integrable nature in terms of the coprimeness property.
We also prove that the Toda-like equations can be expressed as mutations of a seed in the sense of the Laurent phenomenon algebra. |
|