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

著者情報

キーワード: Fuchsian equation, Frobenius method, Riemann-Hilbert problem, normal form, resonance

ジャーナルフリー

2008 年 60 巻 1 号 p. 237-263

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

詳細

抄録

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.