2017/10/10 by Anton Kutlin, Kutlin, A. G.
Chemistry · Mathematics · Physics and Astronomy · #34E20 #Differential Equations and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Surfactants and Colloidal Systems
paper · pdf · doi:10.48550/arxiv.1710.03426
openalex publication_date 2017/10/10 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28
We consider the phase-integral method applied to an arbitrary linear ordinary second-order differential equation with non-analytical coefficients. We propose a universal technique based on the Frobenius method which allows to obtain new exact relation between connection matrices associated with its general solution. The technique allows the reader to write an exact algebraic equation for the Stokes constants provided the differential equation has at most one regular singular point in a finite area of the complex plane. We also propose a way to write approximate relations between Stokes constants in case of multiple regular singular points located far away from each other. The well-known Budden problem is solved with help of this technique as an illustration of its usage. To access the HTML version of the paper & discuss it with the author, visit https://enabla.com/pub/607.