JMP  Vol.5 No.6 , April 2014
Propagation of Dark Solitary Waves in the Korteveg-Devries-Burgers Equation Describing the Nonlinear RLC Transmission
Author(s) Serge Doka Yamigno*
ABSTRACT

We investigate the propagation of dark solitons in a nonlinear dissipative electrical line. We show that the dynamics of the line is reduced to an expanded Korteweg-de Vries-Burgers (KdVB) equation. By applying the perturbation theory to the KdVB equation, we obtain soliton-like pulse solutions. The numerical simulations of the discrete equation are carried out and show the possibility of the founding solution to spread through the line. The effect of the dissipation through soliton is also shown. A chaotic-like behavior can take place in the system during the propagation of dark solitons through the line.


Cite this paper
Yamigno, S. (2014) Propagation of Dark Solitary Waves in the Korteveg-Devries-Burgers Equation Describing the Nonlinear RLC Transmission. Journal of Modern Physics, 5, 394-401. doi: 10.4236/jmp.2014.56051.
References
[1]   Remoissenet, M. (1999) Waves Called Solitons. 3rd Edition, Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-662-03790-4

[2]   Hirota, R. and Suzuki, K. (1970) Journal of the Physical Society of Japan, 28, 1366-1367.
http://dx.doi.org/10.1143/JPSJ.28.1366

[3]   Lonngren, K.E. and Scott, A.C. (1978) Solitons in Action. Academic, New York.

[4]   Reddy, M., Martin, S.C., Molnar, A.C., Muller, R.E., Smith, R.P., Siegel, P.H., Mondry, M.J., Rodwell, M.J.W., Kroemer, H. and Allen Jr., S.J. (1997) IEEE Electron Device Letters, 18, 218-221. http://dx.doi.org/10.1109/55.568771

[5]   Jaeger, I., Kalinowski, D., Stohr, A., Stiens, J., Vounckx, R. and Jager, D. (2007) Microwave and Optical Technology Letters, 49, 2907-2909. http://dx.doi.org/10.1002/mop.22902

[6]   Kivshar, Y.S. and Agrawal, G.P. (2013) Optical Solitons: From Fibers to Photonic Crystals. Academic, New York.

[7]   Sekulic, D.L., Sataric, B.M., Tuszynski, J.A. and Sataric, M.V. (2011) European Physical E: Soft Matter, 34, 49.
http://dx.doi.org/10.1140/epje/i2011-11049-0

[8]   Sekulic, D.L. and Sataric, M.V. (2012) 28th International Conference on Microelectronics-MIEL. in press.

[9]   Marquie, P., Bilbault, J.M. and Remoissenet, M. (1994) Physical Review E, 49, 828-835.
http://dx.doi.org/10.1103/PhysRevE.49.828

[10]   Marquie, P., Bilbault, J.M. and Remoissenet, M. (1995) Physical Review E, 51, 6127-6133.
http://dx.doi.org/10.1103/PhysRevE.51.6127

[11]   Yemélé, D., Marquie, P. and Bilbault, J.M. (2003) Physical Review E, 68, 016605-016616.
http://dx.doi.org/10.1103/PhysRevE.68.016605

[12]   Zhang, Z.Y. (2013) Turkish Journal of Physics, 37, 259-267. http://dx.doi.org/10.3906/fiz-1205-13

[13]   Zhang, Z.Y., Liu, Z.H., Miao, X.J. and Chen, Y.Z. (2010) Applied Mathematics and Computation, 216, 3064-3072.
http://dx.doi.org/10.1016/j.amc.2010.04.026

[14]   Abdoulkary, S., Ousmanou, Mohamadou, A. and Beda, T. (article submitted in CPB 2012).

[15]   Wang, M.L., Zhou, Y.B. and Li, Z.B. (1996) Physics Letters A, 216, 67-75.
http://dx.doi.org/10.1016/0375-9601(96)00283-6

[16]   Yan, Z.Y. and Zhang, H. (2001) Physics Letters A, 285, 355-362. http://dx.doi.org/10.1016/S0375-9601(01)00376-0

[17]   Abdoulkary, S., Mohamadou, A. and Beda, T. (2011) Communications in Nonlinear Science and Numerical Simulation, 16, 3525-3532. http://dx.doi.org/10.1016/j.cnsns.2010.12.029

[18]   Shang, Y., Huang, H. and Yuan, W.J. (2008) Applied Mathematics and Computation, 200, 110-122.
http://dx.doi.org/10.1016/j.amc.2007.10.059

[19]   Wang, Q., Chen, Y. and Zhan, H.Q. (2005) Chaos, Solitons and Fractals, 25, 1019-1028.
http://dx.doi.org/10.1016/j.chaos.2005.01.039

[20]   Yan, C. (1996) Physics Letters A, 224, 77-84. http://dx.doi.org/10.1016/S0375-9601(96)00770-0

[21]   Liu, S.K., Fu, Z.T., Liu, S.D. and Zhao, Q. (2001) Physics Letters A, 289, 69-74.
http://dx.doi.org/10.1016/S0375-9601(01)00580-1

[22]   Zhou, Y.B., Wang, M.L. and Wang, Y.M. (2003) Physics Letters A, 308, 31-36.
http://dx.doi.org/10.1016/S0375-9601(02)01775-9

[23]   Sekulic, D.L., Sataric, M.V., Zivanov, M.B. and Bajic, J.S. (2012) EEE-Kaunas, Technologija, 121, 53-58.

[24]   Sekulic, D.L. and Zivanov, M.B. (2012) MIPRO.
http://mipro-proceedings.com/sites/mipro-proceedings.com/files/upload/meet/meet_046.pdf

[25]   Peyrard, M. and Dauxois, T. (2004) Physique des Solitons. EDP Sciences/CNRS Editions, Les Ulis.

[26]   Kivshar, Y.S. and Malomed, B.A. (1989) Reviews of Modern Physics, 61, 763-915.

[27]   Essimbi, B.Z. and Jager, D. (2010) Physica Scripta, 81, Article ID: 035801.
http://dx.doi.org/10.1088/0031-8949/81/03/035801

[28]   Kivshar, Y.S. and Luther-Davies, B. (1998) Physics Reports, 298, 81-197.
http://dx.doi.org/10.1016/S0370-1573(97)00073-2

[29]   Weiner, A.M. (1992) Optical Solitons: Theory and Experiment. Cambridge University, Cambridge.

[30]   Zhang, X.F., Yang, Q., Zhang, J.F., Chen, X.Z. and Liu, W.M. (2008) Physical Review A, 77, 023613-023621.
http://dx.doi.org/10.1103/PhysRevA.77.023613

[31]   Luther-Davies, B. and Yang, X.P. (1992) Optics Letters, 17, 1755-1757. http://dx.doi.org/10.1364/OL.17.001755

[32]   Swartzlander Jr., G.A. (1992) Optics Letters, 17, 493-495. http://dx.doi.org/10.1364/OL.17.000493

[33]   Luther-Davies, B. and Yang, X.P. (1992) Optics Letters, 17, 496-498. http://dx.doi.org/10.1364/OL.17.000496

[34]   Krokel, D., Halas, N.J., Giuliani, G. and Grischkowsky, D. (1988) Physical Review Letters, 60, 29-32.
http://dx.doi.org/10.1103/PhysRevLett.60.29

[35]   Kivshar, Y.S., Haelterman, M., Emplit, P. and Hamaide, J.P. (1994) Optics Letters, 19, 19-21.
http://dx.doi.org/10.1364/OL.19.000019

[36]   Ablowitz, M.J., Hammack, J., Henderson, D. and Schober, C.M. (2001) Physica D: Nonlinear Phenomena, 152-153, 416-433. http://dx.doi.org/10.1016/S0167-2789(01)00183-X

 
 
Top