An elementary proof of the Voros connection formula for WKB solutions to the Airy equation with a large parameter

2022/05/06 by Aoki, Takashi, Suzuki, Takao, Uchida, Shofu · 1 citation
#33C05 #34E05 #34E15 #34E20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.02988

Abstract

The Voros connection formula for WKB solutions to the Airy equation with a large parameter is proved by using cubic equations. Some parts of the results are generalized to the Pearcey system, which is a two-variable version of the Airy equation, is given.

Cited by

• Exact WKB analysis for dynamical and geometric exponents in generalized and nonlinear Landau-Zener transitions

Related

• The Borel transform of the WKB solution to the Pearcey system
• The Generating Formula for The Solutions to The Associativity Equations
• Voros coefficients of the third Painelv'e equation and parametric Stokes phenomena
• Voros Coefficients and the Topological Recursion for a Class of the Hypergeometric Differential Equations associated with the Degeneration of the 2-dimensional Garnier System
• Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions