Characteristic determinants for a second order difference equation on the half-line arising in hydrodynamics

2024/05/02 by Yuri Latushkin, Latushkin, Yuri, Shibi Vasudevan +1
Mathematics · #34L40 #35B35 #35P99 #35Q31 #35Q35 #40A15 #47A10 #47B36 #47G10 #76E05 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2405.01135

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the point spectrum of a second order difference operator with complex potential on the half-line via Fredholm determinants of the corresponding Birman-Schwinger operator pencils, the Evans and the Jost functions. An application is given to instability of a generalization of the Kolmogorov flow for the Euler equation of ideal fluid on the two dimensional torus.

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