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arXiv · 2505.07466

On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method

S. A. Avdonin·V. S. Mikhaylov·K. B. Nurtazina
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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'.

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S. A. Avdonin, V. S. Mikhaylov, K. B. Nurtazina. 2025-05-12. On inverse dynamical and spectral problems for the wave and Schr\"odinger equations on finite trees. The leaf peeling method. https://doi.org/10.1007/s10958-017-3388-2

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