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Shestopalov, Yury

Open this publication in new window or tab >>Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line### Smirnov, Yuri

### Smolkin, Eugene

### Shestopalov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Blackwell Publishing Ltd, 2019
##### Keywords

nonlinear waveguide, numerical method, TE polarization, the diffraction problem, Dielectric waveguides, Numerical methods, Analytical and numerical solutions, Diffraction problem, Kerr nonlinearity, Nonlinear metals, Nonlinear waveguides, Numerical results, TE polarizations, Transmitted field, Diffraction
##### National Category

Mathematics Other Engineering and Technologies
##### Identifiers

urn:nbn:se:hig:diva-30478 (URN)10.1029/2018RS006629 (DOI)000458731300012 ()2-s2.0-85060646358 (Scopus ID)
#####

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##### Projects

Largescale
##### Funder

Swedish Institute
##### Note

Department of Mathematics and Supercomputing, Penza State University, Russian Federation.

Department of Mathematics and Supercomputing, Penza State University, Russian Federation.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.

The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

Funding agencies:

- Ministry of Education and Science of the Russian Federation Grant no. 1.894.2017/4.6

- University of Gavle, Sweden

Available from: 2019-08-09 Created: 2019-08-09 Last updated: 2019-08-09Bibliographically approvedOpen this publication in new window or tab >>Inverse Scattering and Imaging Using Second Order Optical Nonlinearities### Khulbe, Manisha

### Tripathy, Malay Ranjan

### Parthasarathy, Harish

### Shestopalov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); ### Lagovsky, Boris

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_1_j_idt188_j_idt202",{id:"formSmash:j_idt184:1:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2019 (English)In: 2019 6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, IEEE, 2019, p. 1086-1089Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

IEEE, 2019
##### Keywords

Inverse scattering, least square estimation techniques, Optical nonlinearity, parameter extraction, permeability, permittivity, RF imaging, Electromagnetic fields, Electromagnetic wave diffraction, Mechanical permeability, Parameter estimation, Perturbation techniques, Signal processing, Least square estimation, Perturbation theory, Scattered electromagnetic fields, Second order optical nonlinearity, Third-order optical nonlinearities, Nonlinear optics
##### National Category

Signal Processing
##### Identifiers

urn:nbn:se:hig:diva-30501 (URN)10.1109/SPIN.2019.8711652 (DOI)000470844100209 ()2-s2.0-85066895033 (Scopus ID)9781728113791 (ISBN)
##### Conference

6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, 7-8 March 2019, Noida, India
#####

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##### Note

Ambedkar Institute of Advanced Communication Technologies and Research (AIACTR), Delhi, India.

Amity School of Engineerng and Technology, Amity University, Noida, India.

Netaji Subhash Institute of Technology (NSIT), N. Delhi, India.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.

Russian Technological University, MIREA, Moscow, Russia.

In this paper a mathematical technique is developed to find the parameters of a medium in terms of its scattered electromagnetic fields. Optical nonlinearity plays an important role in finding the scattering parameters of a medium. Using perturbation theory and nonlinear inverse scattering techniques with first order, second order and third order optical nonlinearity we find scattered electromagnetic fields. Using error minimization techniques parameters are estimated in term of permittivity and permeability up to second order. © 2019 IEEE.

Funding agency:

- DST, New Delhi INT/RUS/RFBR/P-341

Available from: 2019-08-15 Created: 2019-08-15 Last updated: 2019-08-22Bibliographically approvedOpen this publication in new window or tab >>Iterative Gradient Descent Methods for Solving Linear Equations### Shestopalov, Yury

### Samokhin, Alexander

### Samokhina, Anna

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Computational Mathematics and Mathematical Physics, ISSN 0965-5425, E-ISSN 1555-6662, Vol. 59, no 8, p. 1267-1274Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

systems of linear algebraic equations, gradient descent, iterative methods
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:hig:diva-30718 (URN)10.1134/S0965542519080141 (DOI)
#####

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Available from: 2019-10-03 Created: 2019-10-03 Last updated: 2019-10-04Bibliographically approved

Russian Technological University MIREA, Moscow, 119454 Russia.

Russian Technological University MIREA, Moscow, 119454 Russia.

Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia.

The paper presents the results on the use of gradient descent algorithms for constructing iterative methods for solving linear equations. A mathematically rigorous substantiation of the conver- gence of iterations to the solution of the equations is given. Numerical results demonstrating the effi- ciency of the modified iterative gradient descent method are presented.

Open this publication in new window or tab >>New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial### Shestopalov, Yury

### Smolkin, Eugene

### Snegur, Maxim

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738241Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

New Dehli: IEEE, 2019
##### Keywords

dielectric waveguides, differential equations, eigenvalues and eigenfunctions, electromagnetic wave propagation, optical metamaterials, optical waveguides, new propagation regimes, TE waves, nonlinear dielectric metamaterial, circular metal-dielectric waveguide, nonlinear metamaterial medium, Kerr nonlinearity, nonlinear transmission eigenvalue problem, ordinary differential equation, eigenvalues, problem correspond, propagation constants, auxiliary Cauchy problem, Electromagnetic waveguides, Dielectrics, Permittivity, Metamaterials, Electromagnetics, Electromagnetic scattering
##### National Category

Electrical Engineering, Electronic Engineering, Information Engineering Mathematics
##### Identifiers

urn:nbn:se:hig:diva-30555 (URN)10.23919/URSIAP-RASC.2019.8738241 (DOI)2-s2.0-85068617892 (Scopus ID)978-908-25987-5-9 (ISBN)978-908-25987-4-2 (ISBN)978-1-5386-8551-8 (ISBN)
##### Conference

URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India
#####

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Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.

Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.

Department of Mathematics and Supercomputing, Penza State University, Penza, Russi.

We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Open this publication in new window or tab >>On a Method of Solution to Dispersion Equations in Electromagnetics### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli, 2019, article id 8738297Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

New Dehli: , 2019
##### Keywords

eigenvalues and eigenfunctions, electromagnetism, iterative methods, oscillations, polynomials, wave equations, dispersion equations, electromagnetics, DEs describing eigenoscillations, normal waves, layered structures, generalized cylindrical polynomials, possible general approach, explicit forms, eigenoscillations, iterative numerical solution techniques, Mathematical model, Dispersion, Frequency modulation, Zinc, Waveguide theory
##### National Category

Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers

urn:nbn:se:hig:diva-30554 (URN)10.23919/URSIAP-RASC.2019.8738297 (DOI)2-s2.0-85068608591 (Scopus ID)978-908-25987-5-9 (ISBN)978-908-25987-4-2 (ISBN)978-1-5386-8551-8 (ISBN)
##### Conference

URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India
#####

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Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-09-04Bibliographically approved

A possible general approach to the analysis of dispersion equations (DEs) of electromagnetics is presented. The method takes into account the known explicit forms of DEs describing eigenoscillations and normal waves in layered structures and is based on the development of the notion of generalized cylindrical polynomials. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the DE roots and validate iterative numerical solution techniques.

Open this publication in new window or tab >>On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.### Smolkin, Eugene

### Smirnov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 91, article id 102378Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Goubau line, Leaky TE waves, Nonhomogeneous dielectric waveguide, Nonlinear permittivity, Numerical method
##### National Category

Physical Sciences
##### Identifiers

urn:nbn:se:hig:diva-30786 (URN)10.1016/j.wavemoti.2019.102378 (DOI)
#####

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Available from: 2019-10-14 Created: 2019-10-14 Last updated: 2019-10-14Bibliographically approved

Department of Mathematics and Supercomputing, Penza State University, Krasnaya Str. 40, Penza, 440026, Russia.

We consider propagation of leaky waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green’s function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. Conditions under which a finite number of waves can propagate are obtained and the intervals of localization of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiments, two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation regimes are discovered.

Open this publication in new window or tab >>Qualitative Analysis of Quadratic Polynomial Dynamical Systems Associated with the Modeling and Monitoring of Oil Fields### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.### Shakhverdiev, Azizaga

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 40, no 10, p. 1695-1710Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Polynomial quadratic dynamical system, qualitative theory, autonomous equation, singularities, qualitative analysis
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:hig:diva-30719 (URN)10.1134/S1995080219100226 (DOI)
#####

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Available from: 2019-10-03 Created: 2019-10-03 Last updated: 2019-10-04Bibliographically approved

Russian State Geological Prospecting University, Moscow, 117997 Russia.

The behavior and properties of solutions of two-dimensional quadratic polynomial dynamical system on the phase plane of variables and time are considered. A complete qualitative theory is constructed which includes the analysis of all singular points and the features of solutions depending on all parameters of the problem. A main result is that, with the discriminant criteria created on the basis of the growth model constructed in the present study, it is possible to formulate practical recommendations for regulating and monitoring the process of waterflooding and the development of an oil field.

Open this publication in new window or tab >>Regression Methods of Obtaining Angular Superresolution### Lagovsky, B. A.

### Samokhin, A. B.

### Shestopalov, Yury V.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738539Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

New Dehli: IEEE, 2019
##### Keywords

Signal resolution, Image resolution, Signal to noise ratio, Image restoration, Radar, Inverse problems
##### National Category

Other Engineering and Technologies Mathematics
##### Identifiers

urn:nbn:se:hig:diva-30553 (URN)10.23919/URSIAP-RASC.2019.8738539 (DOI)2-s2.0-85068588586 (Scopus ID)978-908-25987-5-9 (ISBN)978-908-25987-4-2 (ISBN)978-1-5386-8551-8 (ISBN)
##### Conference

URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India
#####

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Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22Bibliographically approved

Russian Technological University (MIREA), Moscow, Russia.

Russian Technological University (MIREA), Moscow, Russia.

New methods of signal processing based on nonlinear regression methods are presented. They allow us to restore images of individual objects of group targets with superresolution at signal-to-noise ratios that are significantly lower than those provided by the known methods.

Open this publication in new window or tab >>Trigonometric and cylindrical polynomials and their applications in electromagnetics### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis, 2019
##### Keywords

cylindrical polynomials; dispersion equation; zeros; electromagnetic waves
##### National Category

Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers

urn:nbn:se:hig:diva-30485 (URN)10.1080/00036811.2019.1584290 (DOI)2-s2.0-85062349423 (Scopus ID)
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Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved

Development of the theory of trigonometric polynomials (TPs) is considered that involves generalization of the notion of TP and extension of the methods and results to cylindrical polynomials (CPs). On the basis of the proposed augmentation of TPs and CPs, a general approach is presented to the analysis of guided waves and resonances in electromagnetics and beyond. The method employs the known explicit forms of dispersion equations (DEs) describing eigenoscillations and normal waves in layered structures and is based on the development of the theory of generalized TPs and CPs performed in the study. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the TP and CP zeros and the DE roots and validate iterative numerical solution techniques.

Open this publication in new window or tab >>A nonlinear multiparameter EV problem### Angermann, L.

### Shestopalov, Yury V.

### Smirnov, Y. G.

### Yatsyk, V. V.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Progress In Electromagnetics Research Symposium: PIERS 2017, PIERS 2017: Nonlinear and Inverse Problems in Electromagnetics / [ed] Beilina L., Smirnov Y., Springer New York LLC , 2018, p. 55-70Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer New York LLC, 2018
##### Series

Springer Proceedings in Mathematics & Statistics (PROMS) ; 243
##### Keywords

Dispersion equations, Multi-parameter eigenvalue problems, Nonlinear spectral theory, Dispersion (waves), Integral equations, Inverse problems, Mathematical operators, Nonlinear equations, Wave propagation, Eigenvalue problem, Eigenvalues, Integral equation approaches, Multiparameters, Non-linear media, Nonlinear operator, Spectral theory, Eigenvalues and eigenfunctions
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:hig:diva-27866 (URN)10.1007/978-3-319-94060-1_5 (DOI)2-s2.0-85051146418 (Scopus ID)9783319940595 (ISBN)978-3-319-94060-1 (ISBN)
##### Conference

PIERS 2017
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Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2018-09-06Bibliographically approved

Institut für MathematikTechnische Universität Clausthal, Clausthal-Zellerfeld, Germany.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.

Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.

O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine.

We investigate a generalization of one-parameter eigenvalue problems arising in the theory of wave propagation in waveguides filled with nonlinear media to more general nonlinear multi-parameter eigenvalue problems for a nonlinear operator. Using an integral equation approach, we derive functional dispersion equations (DEs) whose roots yield the desired eigenvalues. The existence of the roots of DEs is proved and their distribution is described.