Abstract
An explicit formula concerning curve intersections equivalent to the time evolution of the periodic discrete Toda lattice (pdTL) is presented. First, the time evolution is realized as a point addition on a hyperelliptic curve, which is the spectral curve of the pdTL, then the point addition is translated into curve intersections. Next, it is shown that the curves which appear in the curve intersections are explicitly given by using the conserved quantities of the pdTL. Finally, the formulation is lifted to the framework of tropical geometry and a tropical geometric realization of the periodic box-ball system is constructed via tropical curve intersections.
| Original language | English |
|---|---|
| Article number | 465203 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 46 |
| Issue number | 46 |
| DOIs | |
| Publication status | Published - 2013 Nov 22 |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)