Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

Inverse Problems in Science and Engineering ◽

10.1080/17415977.2018.1479749 ◽

2018 ◽

Vol 27 (8) ◽

pp. 1081-1119

Author(s):

Hélène Barucq ◽

Chokri Bekkey ◽

Rabia Djellouli

Keyword(s):

Spectral Problem ◽

Mathematical Analysis ◽

Optical Waveguides ◽

Inverse Spectral Problem ◽

Inverse Spectral ◽

Solution Methodology

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Regularized Trace for N-Dimensional Vectorial Sturm-Liouville Operator and Its Application in the Inverse Spectral Problem

Acta Analysis Functionalis Applicata ◽

10.3724/sp.j.1160.2010.00137 ◽

2010 ◽

Vol 12 (2) ◽

pp. 137-142

Author(s):

Chuanfu YANG ◽

Zhenyou HUANG

Keyword(s):

Spectral Problem ◽

Liouville Operator ◽

Inverse Spectral Problem ◽

Regularized Trace ◽

Sturm Liouville ◽

Inverse Spectral

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An Inverse Spectral Problem of Sturm–Liouville Problems with Transmission Conditions

Mediterranean Journal of Mathematics ◽

10.1007/s00009-020-01598-0 ◽

2020 ◽

Vol 17 (5) ◽

Author(s):

Ji-jun Ao ◽

Liang Zhang

Keyword(s):

Spectral Problem ◽

Inverse Spectral Problem ◽

Transmission Conditions ◽

Sturm Liouville ◽

Inverse Spectral

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Solution of the Inverse Spectral Problem for a Rod Weakened by Transverse Cracks by the Levenberg—Marquardt Optimization Algorithm

Mechanics of Solids ◽

10.3103/s0025654419060025 ◽

2019 ◽

Vol 54 (6) ◽

pp. 857-872 ◽

Author(s):

I. M. Lebedev ◽

E. I. Shifrin

Keyword(s):

Spectral Problem ◽

Optimization Algorithm ◽

Inverse Spectral Problem ◽

Transverse Cracks ◽

Levenberg Marquardt ◽

Inverse Spectral

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Some uniqueness results of discontinuous coefficients for the one-dimensional inverse spectral problem

Inverse Problems ◽

10.1088/0266-5611/19/4/306 ◽

2003 ◽

Vol 19 (4) ◽

pp. 871-894 ◽

Author(s):

Mourad Sini

Keyword(s):

Spectral Problem ◽

Inverse Spectral Problem ◽

Discontinuous Coefficients ◽

One Dimensional ◽

Uniqueness Results ◽

Inverse Spectral ◽

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Numerical solution of the inverse spectral problem for Bessel operators

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2010.05.018 ◽

2010 ◽

Vol 235 (1) ◽

pp. 120-136 ◽

Author(s):

Rostyslav Hryniv ◽

Paul Sacks

Keyword(s):

Numerical Solution ◽

Spectral Problem ◽

Inverse Spectral Problem ◽

Bessel Operators ◽

Inverse Spectral

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Solution of the inverse spectral problem of the theory of frequencies of vibrations of many-atom molecules, by least-squares method

Journal of Applied Spectroscopy ◽

10.1007/bf00605808 ◽

1971 ◽

Vol 14 (5) ◽

pp. 652-658

Author(s):

V. A. Dement'ev ◽

L. A. Gribov

Keyword(s):

Least Squares ◽

Spectral Problem ◽

Inverse Spectral Problem ◽

Least Squares Method ◽

Inverse Spectral

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Constructive solution of the inverse spectral problem for the matrix Sturm–Liouville operator

Inverse Problems in Science and Engineering ◽

10.1080/17415977.2020.1729760 ◽

2020 ◽

Vol 28 (9) ◽

pp. 1307-1330 ◽

Author(s):

Natalia P. Bondarenko

Keyword(s):

Spectral Problem ◽

Liouville Operator ◽

Inverse Spectral Problem ◽

Constructive Solution ◽

Sturm Liouville ◽

Inverse Spectral

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Inverse Spectral Problem for the Differential Equation of the Second Order with Singularity

Proceedings of the Eighth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18–23 August, 1997 ◽

10.1515/9783112313923-006 ◽

1998 ◽

pp. 17-24

Keyword(s):

Differential Equation ◽

Spectral Problem ◽

Inverse Spectral Problem ◽

Second Order ◽

Inverse Spectral

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An inverse spectral problem for a fourth-order Sturm–Liouville operator based on trace formulae

Applied Mathematics Letters ◽

10.1016/j.aml.2020.106654 ◽

2021 ◽

Vol 111 ◽

pp. 106654

Author(s):

Xiaoying Jiang ◽

Xiang Xu

Keyword(s):

Spectral Problem ◽

Fourth Order ◽

Liouville Operator ◽

Inverse Spectral Problem ◽

Sturm Liouville ◽

Inverse Spectral ◽

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Numerical solution and stability of the inverse spectral problem for a convolution integro-differential operator

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2020.105298 ◽

2020 ◽

Vol 89 ◽

pp. 105298 ◽

Author(s):

Natalia Bondarenko ◽

Sergey Buterin

Keyword(s):

Differential Operator ◽

Numerical Solution ◽

Spectral Problem ◽

Inverse Spectral Problem ◽

Inverse Spectral

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