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Elliptic parameterization of Pfaff integrable hierarchies in the zero-dispersion limit

Abstract

We show that the dispersionless limits of the Pfaff–KP (also known as the DKP or Pfaff lattice) and the Pfaff–Toda hierarchies admit a reformulation in terms of elliptic functions. In the elliptic form, they look like natural elliptic deformations of the respective dispersionless KP and two-dimensional Toda hierarchies.

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Author information

Correspondence to V. E. Akhmedova.

Additional information

This research was supported in part by the Russian Foundation for Basic Research (Grant No. 14-02-00627) and the Government of the Russian Federation within the framework of the implementation of the 5-100 Program Roadmap of the National Research University Higher School of Economics.

The research of A. V. Zabrodin was also supported in part by the Russian Foundation for Basic Research (Joint Grant No. 14-01-90405-Ukr) and the Program for Supporting Leading Scientific Schools (Grant No. NSh- 1500.2014.2).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 3, pp. 410–422, December, 2015.

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Akhmedova, V.E., Zabrodin, A.V. Elliptic parameterization of Pfaff integrable hierarchies in the zero-dispersion limit. Theor Math Phys 185, 1718–1728 (2015). https://doi.org/10.1007/s11232-015-0374-z

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Keywords

  • integrable hierarchy
  • elliptic function
  • Loewner equation