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Transverse Stability in the Discrete Inductance-Capacitance Electrical Network
Laboratory of Mechanics, Department of Physics, Faculty of Sciences, University of Yaounde I, Yaounde, Cameroon
Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers’ Training College, University of Yaounde I, Yaounde, Cameroon
- 1 Laboratory of Mechanics, Department of Physics, Faculty of Sciences, University of Yaounde I, Yaounde, Cameroon
- 2 Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers’ Training College, University of Yaounde I, Yaounde, Cameroon
Journal of Modern Physics·Volume 04 (2013)·Pages 746–753·Published 13 June 2013·DOI10.4236/jmp.2013.46101
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Abstract
This work investigates the dynamics of modulated waves in a coupled nonlinear LC transmission line. By means of a method based on the semi-discrete limit and in suitably scaled coordinates, we derive the two-dimensional NLS equa tion governing the propagation of slowly modulated waves in the network. The exact transverse solution is found and the analytical criteria of stability of this solution are derived. The condition for which the network can exhibit modula tional instability is also determined. The exactness of this analytical analysis is confirmed by numerical simulations performed on the exact equation of the network.
KeywordsTwo-Dimensional Nonlinear Schrödinger EquationExact Transverse SolutionStabilityModulational Instability
- R. Hirota and K. Suzuki, Journal of the Physical Society of Japan, Vol. 28, 1970, pp. 1366-1367. doi:10.1143/JPSJ.28.1366
- A. C. Scott, “Active and Nonlinear Wave Propagation in Electronics,” Wiley, New York, 1970.
- M. Remoissenet, “Waves Called Solitons,” 2nd Edition, Springer, Berlin, 1996. doi:10.1007/978-3-662-03321-0
- E. Tala-Tebue, A. Kenfack-Jiotsa, M. Hervé Tatchou-Ntemfack and T. C. Kofané, Communication in Theorical Physics, 2013, in Press.
- S. Abdoulkary, T. Beda, S. Y. Doka, F. II Ndzana, L. Kavitha and A. Mohamadou, Journal of Modern Physics, Vol. 3, 2012, pp. 438-446 doi:10.4236/jmp.2012.36060
- A. Kenfack-Jiotsa and E. Tala-Tebue, Journal of the Physical Society of Japan, Vol. 80, 2011, Article ID: 034 003 doi:10.1143/JPSJ.80.034003
- A. B. T. Motcheyo, C. Tchawoua, M. S. Siewe and J. D. T. Tchameu, Communications in Nonlinear Science and Numerical Simulation, Vol. 18, 2013, pp. 946-952. doi:10.1016/j.cnsns.2012.09.005
- P. Marquie, J. M. Bilbault and M. Remoissnet, Physical Review E, Vol. 49, 1994, pp. 828-835. doi:10.1103/PhysRevE.49.828
- P. Marquie, J. M. Bilbault and M. Remoissnet, Physical Review E, Vol. 51, 1995, pp. 6127-6133. doi:10.1103/PhysRevE.51.6127
- D. Y. P. Marquié and J. M. Bilbault, Physical Review E, Vol. 68, 2003, Article ID: 016605. doi:10.1103/PhysRevE.68.016605
- M. Antonova and A. Biswas, Communications in Non-linear Science and Numerical Simulation, Vol. 14, 2009, pp. 734-748. doi:10.1016/j.cnsns.2007.12.004
- S. A. El-Wakil and M. A. Abdou, Chaos, Solitons and Fractals, Vol. 31, 2007, pp. 840-852. doi:10.1016/j.chaos.2005.10.032
- W. Malfliet and W. Hereman, Physica Scripta, Vol. 54, 1996, pp. 563-568. doi:10.1088/0031-8949/54/6/003
- M. Y. Moghaddam, A. Asgari and H. Yazdani, Applied Mathematics and Computation, Vol. 210, 2009, pp. 422-435. doi:10.1016/j.amc.2009.01.002
- E. Fan and H. Zhang, Physical Letters A, Vol. 246, 1998, pp. 403-406. doi:10.1016/S0375-9601(98)00547-7
- R. Hirota, “The Direct Method in Soliton Theory,” Cambridge University Press, Cambridge, 2004. doi:10.1017/CBO9780511543043
- M. T. Darvishi and M. Naja, International Journal of Applied Mathematical Research, Vol. 1, 2012, pp. 1-7.