Riccati equations revisited: linearization and analytic interpretation of instanton-type solutions

DOI10.1007/s11785-020-01033-yOpenAlexW3094528783MaRDI QIDQ2211097

Yoshitsugu Takei

Publication date: 12 November 2020

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-020-01033-y

zbMATH Keywords

linearizationRiccati equationsexact WKB analysisinstanton-type solutions

Mathematics Subject Classification ID

Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (1)

Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries

Cites Work

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• Divergent series, summability and resurgence. III. Resurgent methods and the first Painlevé equation
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• WKB analysis of Painlevé transcendents with a large parameter. I
• Singular-perturbative reduction to Birkhoff normal form and instanton-type formal solutions of Hamiltonian systems
• On an exact WKB approach to Ablowitz-Segur's connection problem for the second Painlevé equation
• Asymptotics of the Instantons of Painlevé I
• On the instanton-type expansions for Painlevé transcendents and elliptic functions
• WKB Analysis and Stokes Geometry of Differential Equations
• On the formation of singularities of solutions of nonlinear differential systems in anti-Stokes directions.

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