On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method
Analysis of PDEs
2025-05-13 v1 Classical Analysis and ODEs
Spectral Theory
Abstract
Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum applications. Recently a new effective leaf peeling method has been proposed by S. Avdonin and P. Kurasov \cite{AK} for solving inverse problems on trees (graphs without cycles). It allows recalculating efficiently the inverse data from the original tree to the smaller trees, `removing' leaves step by step up to the rooted edge. In this paper we describe the main step of the spectral and dynamical versions of the peeling algorithm -- recalculating the inverse data for the `peeled tree'.
Cite
@article{arxiv.2505.07466,
title = {On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method},
author = {S. A. Avdonin and V. S. Mikhaylov and K. B. Nurtazina},
journal= {arXiv preprint arXiv:2505.07466},
year = {2025}
}