Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148687 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources / G. Burlak, V. Rabinovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 57 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730155795939328 |
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| author | Burlak, G. Rabinovich, V. |
| author_facet | Burlak, G. Rabinovich, V. |
| citation_txt | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources / G. Burlak, V. Rabinovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 57 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the field eigenfrequencies and the retardation time that become the coupled variables. The main features of the technique are illustrated by examples of the moving source fields in the plasma and the Cherenkov radiation. It is emphasized that the deeper insight to the wave effects in dispersive case already requires the explicit formulation of the dispersive material model. As the advanced application we have considered the Doppler frequency shift in a complex single-resonant dispersive metamaterial (Lorenz) model where in some frequency ranges the negativity of the real part of the refraction index can be reached. We have demonstrated that in dispersive case the Doppler frequency shift acquires a nonlinear dependence on the modulating frequency of the radiated particle. The detailed frequency dependence of such a shift and spectral behavior of phase and group velocities (that have the opposite directions) are studied numerically.
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| first_indexed | 2025-12-07T19:18:55Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148687 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:18:55Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Burlak, G. Rabinovich, V. 2019-02-18T17:54:31Z 2019-02-18T17:54:31Z 2012 Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources / G. Burlak, V. Rabinovich // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 57 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 78A25; 78A35 DOI: http://dx.doi.org/10.3842/SIGMA.2012.096 https://nasplib.isofts.kiev.ua/handle/123456789/148687 The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit expressions for the field amplitudes and simple relations for the field eigenfrequencies and the retardation time that become the coupled variables. The main features of the technique are illustrated by examples of the moving source fields in the plasma and the Cherenkov radiation. It is emphasized that the deeper insight to the wave effects in dispersive case already requires the explicit formulation of the dispersive material model. As the advanced application we have considered the Doppler frequency shift in a complex single-resonant dispersive metamaterial (Lorenz) model where in some frequency ranges the negativity of the real part of the refraction index can be reached. We have demonstrated that in dispersive case the Doppler frequency shift acquires a nonlinear dependence on the modulating frequency of the radiated particle. The detailed frequency dependence of such a shift and spectral behavior of phase and group velocities (that have the opposite directions) are studied numerically. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html.
 The work of authors is partially supported by PROMEP, grant Redes CA 2011–2012. The work of G.B. is partially supported by CONACyT grant 169496. The work of V.R. was partially supported by CONACyT grant 179872. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources Article published earlier |
| spellingShingle | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources Burlak, G. Rabinovich, V. |
| title | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_full | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_fullStr | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_full_unstemmed | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_short | Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources |
| title_sort | time-frequency integrals and the stationary phase method in problems of waves propagation from moving sources |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148687 |
| work_keys_str_mv | AT burlakg timefrequencyintegralsandthestationaryphasemethodinproblemsofwavespropagationfrommovingsources AT rabinovichv timefrequencyintegralsandthestationaryphasemethodinproblemsofwavespropagationfrommovingsources |