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Journal of Dynamical and Control Systems

, Volume 26, Issue 1, pp 149–158 | Cite as

A Note on the Convergence of Multivariate Formal Power Series Solutions of Meromorphic Pfaffian Systems

  • Renat GontsovEmail author
  • Irina Goryuchkina
Article
  • 38 Downloads

Abstract

Here, we present some complements to theorems of R. Gerard and Y. Sibuya, on the convergence of multivariate formal power series solutions of nonlinear meromorphic Pfaffian systems. Their most known results concern completely integrable systems with non-degenerate linear parts, whereas we consider some cases of non-integrability and degeneracy.

Keywords

Meromorphic Pfaffian PDEs system Formal power series solution Convergence 

Notes

Funding Information

The first author was supported by the Russian Foundation for Basic Research (grant nos. 16-51-150005 and 17-01-00515).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Information Transmission Problems of the Russian Academy of SciencesMoscowRussia
  2. 2.Moscow Power Engineering InstituteMoscowRussia
  3. 3.Keldysh Institute of Applied Mathematics of the Russian Academy of SciencesMoscowRussia

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