Dispersionless version of multi-component Pfaff-Toda hierarchy
Year: 2025
Type: preprint
Abstract: We consider the dispersionless limit of the recently introduced multi-component Pfaff-Toda hierarchy. Its dispersionless version is a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the F-function). They are obtained as limiting cases of bilinear equations of the Hirota-Miwa type. The analysis of the Pfaff-Toda hierarchy is substantially simplified by using the observation that the full (not only dispersionless) N-component Pfaff-Toda hierarchy is actually equivalent to the 2N-component DKP hierarchy. In the dispersionless limit, there is an elliptic curve built in the structure of the hierarchy, with the elliptic modular parameter being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization the hierarchy acquires a compact and especially nice form.
Source: arXiv (Cornell University)
Authors: Savchenko, A., Zabrodin, A.
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117753938
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