A Note on the Convergence of Multivariate Formal Power Series Solutions of Meromorphic Pfaffian Systems
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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.
KeywordsMeromorphic Pfaffian PDEs system Formal power series solution Convergence
The first author was supported by the Russian Foundation for Basic Research (grant nos. 16-51-150005 and 17-01-00515).
- 4.Glutsyuk A. Confluence of singular points and the non-linear Stokes phenomena. Trans Mosccow Math Soc. 2001:49–95.Google Scholar
- 5.Iwasaki K, Kimura H, Shimomura S, Yoshida M, Vol. E16. From Gauss to Painlevé. A modern theory of special functions. Aspects math. Braunschweig: Friedr. Vieweg & Sohn; 1991.Google Scholar
- 8.Ploski A. Formal and convergent solutions of analytic equations. Analytic and algebraic geometry 2. Lódź University Press; 2016. p. 161–73.Google Scholar