Dispersionless limits of KP, Toda, and Pfaff-type hierarchies possess a dynamical algebraic curve (genus 0 or 1) that can be uniformized by rational, trigonometric, or elliptic functions.
Zabrodin,Dispersionless limit of the B-Toda hierarchy, Analysis and Mathemat- ical Physics14(2024) 112, arXiv:2401.05919
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Integrable hierarchies with zero dispersion and elliptic curves
Dispersionless limits of KP, Toda, and Pfaff-type hierarchies possess a dynamical algebraic curve (genus 0 or 1) that can be uniformized by rational, trigonometric, or elliptic functions.