Journal of the Mathematical Society of Japan

Singular solutions of nonlinear partial differential equations with resonances

Akira SHIRAI and Masafumi YOSHINO

Full-text: Open access

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.

Article information

Source
J. Math. Soc. Japan, Volume 60, Number 1 (2008), 237-263.

Dates
First available in Project Euclid: 24 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1206367962

Digital Object Identifier
doi:10.2969/jmsj/06010237

Mathematical Reviews number (MathSciNet)
MR2392010

Zentralblatt MATH identifier
1136.35008

Subjects
Primary: 34M35: Singularities, monodromy, local behavior of solutions, normal forms
Secondary: 35L40: First-order hyperbolic systems 35Q15: Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]

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

Citation

YOSHINO, Masafumi; SHIRAI, Akira. Singular solutions of nonlinear partial differential equations with resonances. J. Math. Soc. Japan 60 (2008), no. 1, 237--263. doi:10.2969/jmsj/06010237. https://projecteuclid.org/euclid.jmsj/1206367962


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References

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