Etudes for the inverse spectral problem [PDF]
Journal of the London Mathematical Society, 2023 AbstractIn this note, we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second‐order differential equations on a half‐line. Our goal is to extend the classical results developed in the work of Marchenko, Gelfand–Levitan, and Krein to broader classes of canonical systems and to illustrate the solution
Makarov, Nikolai G., Poltoratski, Alexei
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The inverse spectral problem for periodic conservative multi-peakon solutions of the Camassa-Holm equation [PDF]
International mathematics research notices, 2018 We solve the inverse spectral problem associated with periodic conservative multi-peakon solutions of the Camassa-Holm equation. The corresponding isospectral sets can be identified with finite dimensional tori.Comment: 18 pages, 1 ...
Eckhardt, Jonathan, Kostenko, Aleksey
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INVERSE SPECTRAL PROBLEM [PDF]
Theoretical & Applied Science, 2018 S. Zhanatauov
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An inverse spectral problem for second-order functional-differential pencils with two delays [PDF]
Applied Mathematics and Computation, 2020 We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary condition.
S. A. Buterin +2 more
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Inverse spectral problem for a third-order differential operator with non-local potential [PDF]
Journal of Differential Equations, 2020 Spectral problem for a self-adjoint third-order differential operator with non-local potential on a finite interval is studied. Elementary functions that are analogues of sines and cosines for such operators are described. Direct and inverse problems for
V. Zolotarev
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Constructive solution of the inverse spectral problem for the matrix Sturm–Liouville operator [PDF]
, 2020 An inverse spectral problem is studied for the matrix Sturm–Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the considered inverse ...
N. Bondarenko
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Inverse spectral problem for Sturm - Liouville operator with prescribed partial trace
Ufimskii Matematicheskii Zhurnal, 2020 . This work is aimed at studying optimization inverse spectral problems with a so-called incomplete spectral data. As incomplete spectral data, the partial traces of the Sturm-Liouville operator serve.
N. Valeev, Yavdat Il'yasov
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On nonlinear boundary value problem corresponding to N-dimensional inverse spectral problem [PDF]
Journal of Differential Equations, 2018 We establish a relationship between an inverse optimization spectral problem for N-dimensional Schr\"odinger equation $ -\Delta \psi+q\psi=\lambda \psi $ and a solution of the nonlinear boundary value problem $-\Delta u+q_0 u=\lambda u- u^{\gamma-1},~~u ...
Yavdat S Il'yasov, N. Valeev
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An inverse spectral problem for Sturm–Liouville operators with frozen argument [PDF]
Journal of Mathematical Analysis and Applications, 2017 We consider second order linear differential operators possessing a term depending on the unknown function with a fixed argument and study the uniqueness of recovering the operators from the spectrum.
N. Bondarenko, S. Buterin, S. Vasiliev
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Estimates of complex eigenvalues and an inverse spectral problem for the transmission eigenvalue problem [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2017 This work deals with the interior transmission eigenvalue problem: $y'' + {k^2}\eta \left( r \right)y = 0$ with boundary conditions ${y\left( 0 \right) = 0 = y'\left( 1 \right)\frac{{\sin k}}{k} - y\left( 1 \right)\cos k},$ where the function $\eta(r ...
Xiao‐Chuan Xu +3 more
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