Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-29T04:55:53.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic behavior of the (3+1)-dimensional generalized Johnson model in a dusty plasma

Published online by Cambridge University Press:  11 August 2014

Hui-Ling Zhen ,
Bo Tian ,
Wen-Rong Sun  and
Zhao Tan
Hui-Ling Zhen
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Bo Tian*
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Wen-Rong Sun
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Zhao Tan
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study the (3+1)-dimensional generalized Johnson model, which can be used to describe the dust-ion-acoustic waves in a cosmic unmagnetized dusty plasma, and its perturbed model, which can be found in an unmagnetized dusty plasma for the electron temperature below the Curie temperature. (I) For the original model: Bilinear form and soliton solutions are obtained. Amplitude of the one soliton reaches the maximum when the equilibrium electron (ne0) and ion (ni0) densities take certain values which correspond with ne0/ni0 = 2. Overtaking and head-on interactions between the two solitons are given. (II) For the perturbed model: Phase projections are given numerically. Via the spectral analysis, two kinds of chaotic motions, i.e., the weak and developed chaos, are investigated. Largest Lyapunov exponents and power spectra are investigated to corroborate that those motions are indeed chaotic. Dynamic behavior of such a perturbed model varying with the external perturbation is different when the nonlinear term changes. With the damped term considered, two kinds of periodic motions are studied, and spectra of those periodic motions are also given. Through the comparison between the chaotic motions and periodic ones, possible chaotic or periodic motions in the perturbed model can be predicted.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 905810113
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Basko, D. M. 2011 Ann. Phys.-Berlin 326, 1577.CrossRefGoogle Scholar
Beiglböck, W., Eckmann, J. P., Grosse, H., Loss, M., Smirnov, S., Takhtajan, L. and Yngvason, J. 2000 Concepts and Results in Chaotic Dynamics. Berlin: Springer.Google Scholar
Bergland, G. D. 1969 IEEE Spectrum 6, 228.Google Scholar
Blyuss, K. B. 2000 Rep. Math. Phys. 46, 47.Google Scholar
Cao, H. J., Seoane, J. M. and Sanjuán, A. F. 2007 Chaos Soliton. Fract. 34, 197.Google Scholar
Choi, C. R., Ryu, C. M., Lee, N. C., Lee, D. Y. and Kim, Y. 2005 Phys. Plasmas 12, 072301.Google Scholar
Corsi, L. and Gentile, G. 2012 Commun. Math. Phys. 316, 489.Google Scholar
Dubinov, A. E. and Kolotkov, D. Y. 2012 High Energ. Chem. 46, 349.Google Scholar
Duha, S. S., Shikia, B. and Mamun, A. A. 2011 Pramana-J. Phys. 77, 357.CrossRefGoogle Scholar
Ekeberg, J. 2003 Theory and Modelling of Magnetosonic Solitons in Space Plasma. New York: Elsevier.Google Scholar
El-Tantawy, S. A., Moslem, W. M., Sabry, R., El-Labany, S. K., El-Metwally, M. and Schlickeiser, R. 2014 Astrophys. Space Sci. 350, 175.Google Scholar
Fortov, V. E., Ivlev, A. V., Khrapak, S. A., Khrapak, A. G. and Morfill, G. E. 2005 Phys. Rep. 421, 1.Google Scholar
Gao, Y. T. and Tian, B. 2006 Phys. Plasmas 13, 120703.Google Scholar
Gao, Y. T. and Tian, B. 2006 Phys. Lett. A 349, 314.Google Scholar
Gao, Y. T. and Tian, B. 2006 Phys. Plasmas 13, 112901.CrossRefGoogle Scholar
Higuchi, M. and Fukushima, K. 1998 Chaos Solitons Fract. 9, 845.Google Scholar
Hirota, R. 2004 The Direct Method in Soliton Theory. Cambridge: Cambridge Univ. Press.Google Scholar
Hirota, R. 1971 Phys. Rev. Lett. 27, 1192.Google Scholar
Hirsch, M. W., Smale, S. and Devaney, R. L. 2004 Differential equations, Dynamical Systems, and an Introduction to Chaos. New York: Elsevier.Google Scholar
Husko, C. A., Combrié, S., Cloman, P., Zhen, J. J., Rossi, A. D. and Wong, C. W. 2013 Nature 3, 01100.Google Scholar
Infeld, E. and Rolands, G. 1990 Nonlinear Waves, Soliton and Chaos. Cambridge: Cambridge Univ. Press.Google Scholar
Jitomirskaya, S. and Marx, C. A. 2012 Geom. Funct. Anal. 22, 1407.Google Scholar
Kumar, H., Malik, A. and Chand, F. 2013 P. Indian AS-Math Sci. 80, 361.Google Scholar
Kuznetsov, E. A., Rubenchik, A. M. and Zakharov, V. E. 1986 Phys. Rep. 142, 103.Google Scholar
Lalescu, C. C., Meneveau, C. and Eyink, G. L. 2013 Phys. Rev. Lett. 110, 084102.Google Scholar
Laptyeva, T. V., Bodyfelt, J. D., Krimer, D. O. and Flach, S. 2010 Europhys. Lett. 91, 30001.CrossRefGoogle Scholar
Li, Y. and Sattinger, D. H. 1999 J. Math. Fluid Mech. 1, 117.CrossRefGoogle Scholar
Liu, H. F., Wang, S. Q. and Yang, F. Z. 2013 Astrophys. Space Sci. 347, 139.Google Scholar
Malkov, M. A. 1996 Phys. D 95, 62.CrossRefGoogle Scholar
Mendis, D. A. 2002 Plasma Sources Sci. Tech. 11, A219.Google Scholar
Moon, H. T. 1990 Phys. Rev. Lett. 64, 412.CrossRefGoogle Scholar
Morfill, G. E., Tsytovich, V. N. and Thomas, H. 2003 Plasma Phys. Rep. 29, 682.CrossRefGoogle Scholar
Moslem, W. 2006 Phys. Lett. A 351, 290.Google Scholar
Mulansky, M., Ahnert, K., Pikovsky, A. and Shepelyansky, D. L. 2011 J. Stat. Phys. 145, 1256.Google Scholar
Narayanan, M., Tong, S., Ma, B. H., Liu, S. S. and Balachandran, U. 2012 Phys. Plasmas, 100, 022907.Google Scholar
Nokazi, K. and Bekki, N. 1983 Phys. Rev. Lett. 50, 1226.Google Scholar
Popel, S., Losseva, T., Golub, A., Merlino, R. and Andreev, S. 2005 Contrib. Plasma Phys. 45, 461.Google Scholar
Ryskin, N. M. and Titov, V. N. 2011 Tech. Phys. 48, 1170.CrossRefGoogle Scholar
Sahu, B., Poria, S. and Roychoudhury, R. 2012 Astrophys. Space Sci. 341, 567.Google Scholar
Sahu, B. and Roychoudhury, R. 2003 Phys. Plasmas 10, 4162.Google Scholar
Scharf, R. and Bishop, A. R. 1992 Phys. Rev. A 46, 6.Google Scholar
Shen, Y. J., Gao, Y. T., Zuo, D. W., Sun, Y. H., Feng, Y. J. and Xue, L. 2014 Phys. Rev. E 89, 062915.CrossRefGoogle Scholar
Shen, Y. J., Gao, Y. T., Yu, X., Meng, G. Q. and Qin, Y. 2014 Appl. Math. Comput. 227, 502.Google Scholar
Shukla, P. K. 2001 Phys. Plasmas 8, 1791.CrossRefGoogle Scholar
Shukla, P. K. and Mamun, A. A. 2002 Introduction to Dusty Plasma Physics. Bristol: IOP Pub.Google Scholar
Sreelatha, K. S. and Joseph, K. B. 1998 Chaos Solitons Fract. 9, 1865.Google Scholar
Stoica, P. and Moses, R. L. 1997 Introduction to Spectral Analysis. New Jersey: Prentice Hall.Google Scholar
Sun, Z. Y., Gao, Y. T., Yu, X. and Liu, Y. 2011a Europhys. Lett. 93, 40004.Google Scholar
Sun, Z. Y., Gao, Y. T., Liu, Y. and Yu, X. 2011b Phys. Rev. E 84, 026606.Google Scholar
Sun, Z. Y., Gao, Y. T., Yu, X. and Liu, Y. 2013 Phys. Lett. A 377, 3283.Google Scholar
Taylor, J. R. 1992 Optical Solitons Theory and Experiment. Cambridge: Cambridge Univ. Press.Google Scholar
Tian, B. and Gao, Y. T. 2005 Phys. Plasmas 12, 054701.CrossRefGoogle Scholar
Tian, B. and Gao, Y. T. 2005 Phys. Plasmas 12, 070703.Google Scholar
Tian, B. and Gao, Y. T. 2005a Phys. Lett. A 340, 449.Google Scholar
Tian, B. and Gao, Y. T. 2005b Eur. Phys. J. D 33, 59.Google Scholar
Tsytovich, V. N., Morfill, G. E. and Thomas, H. 2002 Plasma Phys. Rep. 28, 623.Google Scholar
Williams, G. P. 1997 Chaos Theory Tamed. Washington D. C.: Joseph Henry.Google Scholar
Xue, J. K. 2003 Phys. Lett. A 314, 479.Google Scholar
Yang, J. K. and Kaup, D. J. 2000 SIAM J. Appl. Math. 60, 967.Google Scholar
Yu, J., Zhang, W. J. and Gao, X. M. 2007 Chaos Solitons Fract. 33, 1307.Google Scholar
Zheng, D. J., Yeh, W. J. and Symko, O. G. 1989 Phys. Lett. A 140, 225.Google Scholar
Zuo, D. W., Gao, Y. T., Meng, G. Q., Shen, Y. J. and Yu, X. 2014a Non. Dyn. 75, 701.Google Scholar
Zuo, D. W., Gao, Y. T., Sun, Y. H., Feng, Y. J. and Xue, L. 2014b Z. Naturforsch. A, in press, DOI: 10.5560/ZNA.2014-0045.Google Scholar