Bakhoum, Ezzat G.; Toma, Cristian Mathematical transform of traveling-wave equations and phase aspects of quantum interaction. (English) Zbl 1191.35220 Math. Probl. Eng. 2010, Article ID 695208, 15 p. (2010). Summary: The traveling wave equation is an essential tool in the study of vibrations and oscillating systems. This paper introduces an important extension to the Fourier/Laplace transform that is needed for the analysis of signals that are represented by traveling wave equations. Another objective of the paper is to present a mathematical technique for the simulation of the behavior of large systems of optical oscillators. Cited in 27 Documents MSC: 35Q40 PDEs in connection with quantum mechanics PDFBibTeX XMLCite \textit{E. G. Bakhoum} and \textit{C. Toma}, Math. Probl. Eng. 2010, Article ID 695208, 15 p. (2010; Zbl 1191.35220) Full Text: DOI EuDML References: [1] W. H. Hayt and J. A. Buck, Engineering Electromagnetics, McGraw Hill, New York, NY, USA, 2006. [2] R. Feynmam, R. Leighton, and M. Sands, The Feynman Lectures on Physics, vol. 2, Addison Wesley, Reading, Mass, USA, 1977. [3] J. S. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall, Upper Saddle River, NJ, USA, 1990. [4] T. W. Korner, Fourier Analysis, Cambridge University Press, Cambridge, UK, 2nd edition, 1989. [5] J. E. Marsden and M. J. Hoffman, Basic Complex Analysis, W. H. Freeman, New York, NY, USA, 2nd edition, 1987. · Zbl 0644.30001 [6] T. S. Rappaport, Wireless Communications, Prentice Hall, Upper Saddle River, NJ, USA, 1996. [7] V. K. Garg and J. E. Wilkes, Wireless and Personal Communications Systems, Prentice Hall, Upper Saddle River, NJ, USA, 1996. [8] V. K. Garg, Wireless Network Evolution, Prentice Hall, Upper Saddle River, NJ, USA, 2002. [9] E. Bakhoum and C. Toma, “Relativistic short range phenomena and space-time aspects of pulse measurements,” Mathematical Problems in Engineering, vol. 2008, Article ID 410156, 20 pages, 2008. · Zbl 1163.83319 · doi:10.1155/2008/410156 [10] N. Nelipa, Physique des Particules Elementaires, MIR, Moscou, Russia, 1981. [11] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, Cambridge, UK, 1995. [12] A. Toma, S. Pusca, and C. Morarescu, “Spatial aspects of interaction between high-energy pulses and waves considered as suddenly emerging phenomena,” in Proceedings of the 1st International Conference on Computational Science and Its Applications (ICCSA /06), vol. 3980 of Lecture Notes Computer Science, pp. 839-846, Glasgow, UK, May 2006. · Zbl 05497911 · doi:10.1007/11751540_91 [13] P. Sterian and C. Toma, “Methods for presenting key concepts in physics for MS students by photon-MD program,” Bulgarian Journal of Physics, vol. 27, no. 4, pp. 27-30, 2000. [14] Th. Toma, S. Pusca, and C. Morarescu, “Simulating superradiant laser pulses using partial fraction decomposition and derivative procedures,” in Proceedings of the 1st International Conference on Computational Science and Its Applications (ICCSA /06), vol. 3980 of Lecture Notes Computer Science, pp. 779-784, Glasgow, UK, May 2006. · Zbl 05497903 · doi:10.1007/11751540_83 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.