Perturbation Method and Existence of Nonlinearizable Solutions in the Problem of Propagation of a Nonlinear Coupled TE–TE Wave in a Planar Optical Waveguide with Spatial Inhomogeneity of the Medium

Authors: Valovik, D. V.^{Aff1, IDS0965542525701945_cor1}, Dyundyaeva, A. A.^{Aff1, IDS0965542525701945_cor2}, Tikhov, S. V.^{Aff1, IDS0965542525701945_cor3}

Source: Computational Mathematics and Mathematical Physics. 66(2):268-282

A Sylvester equation approach for the computation of zero-group-velocity points in waveguides

Authors: Plestenjak, Bor^{Aff1, Aff2, IDs00466025026568_cor1}, Kiefer, Daniel A.^Aff3, Gravenkamp, Hauke^Aff4

Source: Computational Mechanics: Solids, Materials, Complex Fluids, Fluid-Structure-Interaction, Biological Systems, Micromechanics, Multiscale Mechanics, Additive Manufacturing. 76(5):1443-1456

Nonlinearizing two-parameter eigenvalue problems

Authors: Ringh, Emil, Author, Jarlebring, Elias, Author

Contributors: Ringh, Emil, Author, Jarlebring, Elias, Author

Source: SIAM Journal on Matrix Analysis and Applications. 42(2):775-799

Subject Terms: two-parameter eigenvalue problem, nonlinear eigenvalue problem, multiparameter eigenvalue problem, iterative algorithms, implicit function theorem, Numerical Analysis, Numerisk analys, Tillämpad matematik och beräkningsmatematik, Applied and Computational Mathematics

File Description: print

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291995
https://doi.org/10.1137/19M1274316

On properties and numerical computation of critical points of eigencurves of bivariate matrix pencils

Authors: Plestenjak, Bor^{Aff1, Aff2, IDs10092025006776_cor1}

Source: Calcolo. 63(1)

Finding the Set of Branching Points of a Nonlinear Integral Equation Arising in the Synthesis Problem by a Given Power Directivity Pattern

Authors: Podlevskyi, Bohdan

Source: 2020 IEEE Ukrainian Microwave Week (UkrMW) Ukrainian Microwave Week (UkrMW), 2020 IEEE. :1-4 Sep, 2020

Relation: 2020 IEEE Ukrainian Microwave Week (UkrMW)

On the Existence of Nonlinearizable Solutions of a Nonclassical Two-Parameter Nonlinear Boundary Value Problem: On the existence of nonlinearizable solutions of a nonclassical two-parameter nonlinear boundary value problem

Authors: Martynova, V. Yu.

Source: Differential Equations. 60:445-464

Subject Terms: Maxwell equations, nonlinear permittivity, Parameter dependent boundary value problems for ordinary differential equations, Explicit solutions, first integrals of ordinary differential equations, nonlinearizable solution, Boundary eigenvalue problems for ordinary differential equations, two-parameter eigenvalue problem, integral characteristic equation

File Description: application/xml

Access URL: https://zbmath.org/7891408
https://doi.org/10.1134/s0012266124040049

Nonclassical perturbation approach to a nonlinear multiparameter eigenvalue problem arising in electromagnetics

Authors: Valeria Martynova, Dmitry Valovik

Source: Mathematical Methods in the Applied Sciences. 46:13205-13225

Subject Terms: nonpertubative solutions, Maxwell equations, Maxwell's equations, nonlinear permittivity, ordinary differential equations, nonlinear eigenvalue problem, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, 0101 mathematics, Perturbations of nonlinear operators, 01 natural sciences, integral characteristic equation, two-parameter eigenvalue problem

File Description: application/xml

Access URL: https://zbmath.org/7790782
https://doi.org/10.1002/mma.9244

On the Kronecker Structure of linearization of Cubic Two-Parameter Eigenvalue Problems

Authors: Bora, Niranjan, Borgohain, Bharati

Source: Malaysian Journal of Science (MJS); Vol 44 No 1 (2025): March 2025; 70-86 ; 2600-8688 ; 1394-3065

Subject Terms: Cubic two-parameter eigenvalue problem, Linear two-parameter eigenvalueproblem, linearization, matrix polynomial

File Description: application/pdf

Relation: https://ejournal.um.edu.my/index.php/index/article/view/45991/18200; https://ejournal.um.edu.my/index.php/index/article/view/45991

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https://doi.org/10.22452/mjs.vol44no1.9

On the singular two-parameter eigenvalue problem II: On the singular two-parameter eigenvalue problem. II

Authors: Tomaž Košir, Bor Plestenjak

Source: Linear Algebra and its Applications. 649:433-451

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, Canonical forms, reductions, classification, minimal reducing subspace, singularni dvoparametrični problem lastnih vrednosti, Numerical Analysis (math.NA), 15A18, 15A21, 15A22, 15A69, 65F15, minimalni reducirajoči podprostor, 01 natural sciences, Mathematics - Spectral Theory, stratification, stratifikacija, Multilinear algebra, tensor calculus, singular two-parameter eigenvalue problem, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Matrix pencils, Spectral Theory (math.SP), Kroneckerjeva kanonična oblika, Kronecker canonical form

File Description: application/xml; application/pdf; text/url

Access URL: http://arxiv.org/abs/2110.08836
https://zbmath.org/7553087
https://doi.org/10.1016/j.laa.2022.05.013
https://arxiv.org/abs/2110.08836
https://repozitorij.uni-lj.si/IzpisGradiva.php?id=139719
https://hdl.handle.net/20.500.12556/RUL-139719
https://doi.org/10.1016/j.laa.2022.05.013

Solving two-parameter eigenvalue problems using an alternating method

Authors: Eisenmann, H, Nakatsukasa, Y

Source: Linear algebra and its applications

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, Multilinear algebra, tensor calculus, FOS: Mathematics, Helmholtz equation, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences, two-parameter eigenvalue problem, alternating optimization

File Description: application/xml

Access URL: http://arxiv.org/pdf/2008.03385
http://arxiv.org/abs/2008.03385
https://zbmath.org/7501860
https://doi.org/10.1016/j.laa.2022.02.024
https://arxiv.org/abs/2008.03385
https://ora.ox.ac.uk/objects/uuid:911aa2c5-bbd9-4dbd-a8bb-b591d932d47e
https://doi.org/10.1016/j.laa.2022.02.024
https://hdl.handle.net/21.11116/0000-000D-9A87-D

Surface waves in a Goubau line filled with nonlinear anisotropic inhomogeneous medium

Authors: Smirnov, Yury, Author, Smolkin, Eugen, Author, Shestopalov, Yury, 1953-, Author

Contributors: Smirnov, Yury, Author, Smolkin, Eugen, Author, Shestopalov, Yury, 1953-, Author

Source: Applicable Analysis. 10(17):6172-6190

Subject Terms: Goubau Line, non-polarized azimuthal-symmetric electromagnetic waves, Kerr nonlinearitynonlinear inhomogeneous waveguide, Maxwell's equations, two-parameter eigenvalue problem, numerical method

File Description: print

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-35734

A new algorithm using L-BFGS for two-parameter eigenvalue problems from Lamé's system and simulation

Authors: Özer, Hayati Ünsal, Duran, Ahmet

Source: Volume: 4, Issue: 4448-468
Mathematical Modelling and Numerical Simulation with Applications

Subject Terms: Numerical Analysis, Sayısal Analiz, Matematikte Optimizasyon, Diferansiyel ve İntegral Denklemlerin Sayısal Çözümü, Mathematical Optimisation, Deneysel Analiz, Uygulamalarda Dinamik Sistemler, Simulation, Lamé system, numerical linear algebra and matrix theory, algorithm for two-parameter eigenvalue problem, numerical parameter optimization, Dynamical Systems in Applications, Numerical Solution of Differential and Integral Equations, Experimental Mathematics

File Description: application/pdf

Access URL: https://dergipark.org.tr/tr/pub/mmnsa/issue/88766/1523702

Numerical Study of Propagation of Nonlinear Coupled Surface and Leaky Electromagnetic Waves in a Circular Cylindrical Metal–Dielectric Waveguide: Numerical study of propagation of nonlinear coupled surface and leaky electromagnetic waves in a circular cylindrical metal-dielectric waveguide

Authors: Smirnov, Yu. G., Smol'kin, E. Yu., Snegur, M. O.

Source: Computational Mathematics and Mathematical Physics. 61:1353-1363

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, inhomogeneous waveguide, nonlinear two-parameter eigenvalue problem, Nonlinear boundary value problems for ordinary differential equations, Lasers, masers, optical bistability, nonlinear optics, Antennas, waveguides in optics and electromagnetic theory, Goubau line, Kerr nonlinearity, 01 natural sciences, polarized surface TE and leaky TM waves, Maxwell equations, Maxwell's equations, Electromagnetic theory (general), 0103 physical sciences, Waves and radiation in optics and electromagnetic theory, Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators, 0101 mathematics, Numerical solution of eigenvalue problems involving ordinary differential equations

File Description: application/xml

Perturbation Method in the Theory of Propagation of Two-Frequency Electromagnetic Waves in a Nonlinear Waveguide I: TE-TE Waves: Perturbation method in the theory of propagation of two-frequency electromagnetic waves in a nonlinear waveguide. I: TE-TE waves

Authors: Valovik, D. V.

Source: Computational Mathematics and Mathematical Physics. 61:103-117

Subject Terms: nonlinear permittivity, Perturbations in context of PDEs, perturbation method, Existence problems for PDEs: global existence, local existence, non-existence, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Antennas, waveguides in optics and electromagnetic theory, 01 natural sciences, integral characteristic equation, Sturm-Liouville theory, Maxwell's equations, 0103 physical sciences, nonlinear Sturm-Liouville-type problem, Waves and radiation in optics and electromagnetic theory, PDEs in connection with optics and electromagnetic theory, planar dielectric waveguide, two-parameter eigenvalue problem

File Description: application/xml

Access URL: https://zbmath.org/7319653
https://doi.org/10.1134/s0965542521010097

On the Existence of Nonlinear Coupled Surface TE and Leaky TM Electromagnetic Waves in a Circular Cylindrical Waveguide

Authors: Smirnov, Yu. G.^{Aff1, IDS1063784222070106_cor1}, Smolkin, E. Yu.^{Aff1, IDS1063784222070106_cor2}

Source: Technical Physics. 67(6):543-548

Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation: Solving singular generalized eigenvalue problems by a rank-completing perturbation

Authors: Hochstenbach, Michiel E., Mehl, Christian, Plestenjak, Bor

Source: SIAM Journal on Matrix Analysis and Applications. 40:1022-1046

Subject Terms: Differential algebraic equations, Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, singular generalized eigenvalue problem, Singular generalized eigenvalue problem, Perturbation theory of linear operators, double eigenvalues, Canonical forms, reductions, classification, 01 natural sciences, singular pencil, 65F15, 15A18, 15A22, 15A21, 47A55, 65F22, Model updating, Rank-completing perturbation, rank-completing perturbation, Two-parameter eigenvalue problem, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Singular pencil, Quadratic two-parameter eigenvalue problem, Double eigenvalues, model updating, 510 Mathematik, Numerical Analysis (math.NA), Ill-posedness and regularization problems in numerical linear algebra, Guptri, eigenvalue problem, differential algebraic equations, quadratic two-parameter eigenvalue problem, Matrix pencils, two-parameter eigenvalue problem

File Description: application/xml

Access URL: http://arxiv.org/pdf/1805.07657
http://arxiv.org/abs/1805.07657
https://zbmath.org/7122450
https://doi.org/10.1137/18m1188628

Asymptotic Behaviour of the Non-real Pair-Eigenvalues of a Two Parameter Eigenvalue Problem

Authors: Öztürk, Hasen Mekki^{Aff1, IDs1178502301344w_cor1}

Source: Complex Analysis and Operator Theory. 17(4)

On the existence of nonlinear coupled surface TE- and leaky TM-electromagnetic waves in a circular cylindrical waveguide

Authors: Yu.G. Smirnov, E.Yu. Smol'kin

Source: Известия высших учебных заведений. Поволжский регион: Физико-математические науки, Iss 1 (2022)

Subject Terms: inhomogeneous waveguide, goubau line, maxwell's equations, surface waves, leaky waves, coupled waves, nonlinear two-parameter eigenvalue problem, Physics, QC1-999, Mathematics, QA1-939

File Description: electronic resource

Relation: https://doaj.org/toc/2072-3040

Access URL: https://doaj.org/article/0c54774aa852493d96c9b2c24c2c527f

On the singular two-parameter eigenvalue problem II

Authors: Košir, Tomaž, Plestenjak, Bor

Source: Linear algebra and its applications, vol. 649, pp. 433-451, 2022. ; ISSN: 0024-3795

Subject Terms: singular two-parameter eigenvalue problem, Kronecker canonical form, minimal reducing subspace, stratification, singularni dvoparametrični problem lastnih vrednosti, Kroneckerjeva kanonična oblika, minimalni reducirajoči podprostor, stratifikacija, info:eu-repo/classification/udc/512.643:519.6

File Description: application/pdf; text/url

Relation: info:eu-repo/grantAgreement/ARRS//N1-0154; https://plus.cobiss.net/cobiss/si/sl/bib/111311363

Availability: https://repozitorij.uni-lj.si/IzpisGradiva.php?id=139719
https://repozitorij.uni-lj.si/Dokument.php?id=160325&dn=
https://repozitorij.uni-lj.si/Dokument.php?id=160324&dn=
https://plus.cobiss.net/cobiss/si/sl/bib/111311363
https://hdl.handle.net/20.500.12556/RUL-139719

The Homotopy Method for the Complete Solution of Quadratic Two-parameter Eigenvalue Problems

Authors: Dong, Bo^{Aff1, IDs10915021016938_cor1}

Source: Journal of Scientific Computing. 90(1)