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Instanton-type formal solutions for the first Painlevé hierarchy

In: Algebraic Analysis of Differential Equations

Author

Listed:
  • Yoshitsugu Takei

    (Kyoto University, Research Institute for Mathematical Sciences)

Abstract

Instanton-type formal solutions, which will play an important role in the description of Stokes phenomena, are discussed for the first Painlevé hierarchy. We construct instanton-type solutions by using singular-perturbative reduction of a Hamiltonian system to its Birkhoff normal form. The construction of singularperturbative reduction to the Birkhoff normal form is also outlined.

Suggested Citation

  • Yoshitsugu Takei, 2008. "Instanton-type formal solutions for the first Painlevé hierarchy," Springer Books, in: Takashi Aoki & Hideyuki Majima & Yoshitsugu Takei & Nobuyuki Tose (ed.), Algebraic Analysis of Differential Equations, pages 307-319, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-73240-2_25
    DOI: 10.1007/978-4-431-73240-2_25
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