Exact solutions to the Telegraph equation in terms of Airy functions
DOI:
https://doi.org/10.31349/RevMexFis.70.040701Keywords:
Telegraph Equation, Airy functionsAbstract
Two exact different solutions to the Telegraph equation in three-dimensional space are obtained in terms of Airy functions. As a result, these solutions unveil a distinctive propagation pattern along a coordinate that resembles a speed-cone-like coordinate of the system. This unique characteristic leads to effective Schr¨ödinger-like equations, amenable to exact solutions through Airy functions.
References
M. V. Berry and N. L. Balazs, Am. J. Phys. 47 (1979) 264
O. Vallee and M. Soares, Airy functions and applications to physics (Imperial College Press, 2004)
N. Wiersma, N. Marsal, M. Sciamanna and D. Wolfersberger, Sci. Rep. 6 (2016) 35078
Y. Jiang, K. Huang, and X. Lu, Opt. Express 20 (2012) 18579
D. Abdollahpour et al., Phys. Rev. Lett. 105 (2010) 253901
T. Bouchet et al. Sci Rep 12 (2022) 9064
A. Chong et al., Nature Photon 4 (2010) 103
I. Kaminer et al., Phys. Rev. Lett. 108 (2012) 163901
P. Panagiotopoulos et al., Nat Commun 4 (2013) 2622
H. Esat Kondakci and A. F. Abouraddy, Phys. Rev. Lett. 120 (2018) 163901
N. K. Efremidis et al., Optica 6 (2019) 686
S. Chavez-Cerda et al., Opt. Exp. 19 (2011) 16448
J. Baumgartl, M. Mazilu and K. Dholakia, Nature Photon 2 (2008) 675
S. Fu, Y. Tsur, J. Zhou, L. Shemer and A. Arie, Phys. Rev. Lett. 115 (2015) 034501
S. Zhao et al., Sci Rep 4 (2014) 6628
F. A. Asenjo and S. A. Hojman, Eur. Phys. J. Plus 136 (2021) 677
D.-C. Chen et al., Appl. Phys. Lett. 114 (2019) 053504
John D. Kraus, Electromagnetics, Third edition, McGraw-Hill (1984)
W. Hayt, Engineering Electromagnetics, Fifth Edition, McGraw-Hill (1989)
S. V. Marshall, Electromagnetic Concepts and Applications, Firste Edition, Prentice-Hall (1987)
M. Dehghan and A. Shokri, Numer. Methods Partial Differential Eq. 24 (2008) 1080
S. Goldstein, The Quarterly Journal of Mechanics and Applied Mathematics 4 (1951) 129
J. Chen, F. Liu and V. Anh, J. Math. Anal. Appl. 338 (2008) 1364
J. Biazar and M. Eslami, Phys. Lett. A 374 (2010) 2904
S. Kumar, Applied Mathematical Modelling 38 (2014) 3154
T. I. Gombosi et al., Astrophys. J. 403 (1993) 377
F. Huang, Journal of Applied Mathematics 2009 (2009) 890158
G. W. Bluman, Temuerchaolu and R. Sahadevan, J. Math. Phys. 46 (2005) 023505
S. Das, K. Vishal, P. K. Gupta and A. Yildirim, Applied Mathematics and Computation 217 (2011) 7405
M. M. A. Khater an D. Lu, Mod. Phys. Lett. B 35 (2021) 2150324
V. K. Srivastava, M. K. Awasthi, R. K. Chaurasia and M. Tamsir, Modelling and Simulation in Engineering 2013 (2013) 746351
L. Beghin, L. Nieddu and E. Orsingher, J. App. Math. Stoch. Anal. 14 (2001) 11
E. Orsingher and L. Beghin, Probab. Theory Relat. Fields 128 (2004) 141
A. F. Turbin, and I. V. Samoilenko, Ukrainian Mathematical Journal 52 (2000) 1292
A. Borodin and V. Gorin, Ann. Probab. 47 (2019) 4137
V. Borisov and I. Simonenko, J. Phys. I 7 (1997) 923
M. Fabrizio and A. Morro, Electromagnetism of Contin- uous Media (Oxford University Press, 2010)
P. M. Jordan and A. Puri, J. Appl. Phys. 85 (1999) 1273
R. J. Thompson and T. M. Moeller, Phys. Plasmas 19 (2012) 082116
Y. E. Litvinenko and P. L. Noble, Phys. Plasmas 23 (2016) 062901
G. H. Weiss, Physica A 311 (2002) 381
M. D. Kostin, J. Stat. Phys. 45 (1986) 765
A. I. Arbab, Optik 140 (2017) 1010
P. Sancho, Open Sys. & Information Dyn. 7 (2000) 157
S. R. Arridge, Inverse Problems 15 (1999) R41
I. M. Besieris, A. M. Shaarawi and R. W. Ziolkowski, Am. J. Phys. bf 62 (1994) 519
Y. Z. Umul, Optik 247 (2021) 167918
J. Lekner, Eur. J. Phys. 30 (2009) L43
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