• Corpus ID: 246016058

Hermite-Padé approximation and integrability

@article{Doliwa2022HermitePadAA,
  title={Hermite-Pad{\'e} approximation and integrability},
  author={Adam Doliwa and Artur Siemaszko},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.06829}
}
We show that solution to the Hermite–Padé type I approximation problem leads in a natural way to a subclass of solutions of the Hirota (discrete Kadomtsev–Petviashvili) system and of its adjoint linear problem. Our result explains the appearence of various ingredients of the integrable systems theory in application to multiple orthogonal polynomials, numerical algorthms, random matrices, and in other branches of mathematical physics and applied mathematics where the Hermite–Padé approximation… 
1 Citations

Integrability and geometry of the Wynn recurrence

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It is shown that the Wynn recurrence can be incorporated into the theory of integrable systems as a reduction of the discrete Schwarzian Kadomtsev–Petviashvili equation, allowing the geometric meaning of the recurrence to be presented as a construction of the appropriately constrained quadrangular set of points.

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