A. I. Gudimenko, A. V. Likhosherstov, “Application of the Lagrange formula to calculate the eigenvalues of a harmonic chain with dissipation at the boundaries”, Dal'nevost. Mat. Zh., 2025, Volume 25, Number 2,Pages <nobr>232

Application of the Lagrange formula to calculate the eigenvalues of a harmonic chain with dissipation at the boundaries

A. I. Gudimenko^a, A. V. Likhosherstov^ab

^a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
^b V. I. Il'ichev Pacific Oceanological Institute, Far Eastern Branch of RAS, Vladivostok

Abstract: The eigenvalue problem for a dynamic system describing in Schrödinger coordinates the oscillations of a homogeneous harmonic chain with dissipation at the boundaries is considered. The combinatorial Lagrange formula is used to obtain a uniform approximation of the eigenvalues for a sufficiently large number of particles in the chain.

Key words: harmonic chain, Schrödinger coordinates, eigenvalue problem.

UDC: 512.643.5, 517, 933

MSC: Primary 15A18; Secondary 34K11

Received: 01.06.2025
Accepted: 07.11.2025

DOI: 10.47910/FEMJ202516