Singular solutions of nonlinear partial differential equations with resonances

Masafumi YOSHINO; Akira SHIRAI

doi:10.2969/jmsj/06010237

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Singular solutions of nonlinear partial differential equations with resonances

Masafumi YOSHINO, Akira SHIRAI

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Keywords: Fuchsian equation, Frobenius method, Riemann-Hilbert problem, normal form, resonance

JOURNAL FREE ACCESS

2008 Volume 60 Issue 1 Pages 237-263

DOI https://doi.org/10.2969/jmsj/06010237

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Abstract

We present a Frobenius type theorem for a system of nonlinear partial differential equations. Typical application is the normal form theory of a singular vector field. The construction of a singular solution is closely related with a Riemann-Hilbert factorization.

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