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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

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1865-7109
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Volume 72, Issue 7

Issues

Rational Solutions and Lump Solutions of the Potential YTSF Equation

Hong-Qian Sun / Ai-Hua Chen
  • Corresponding author
  • College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, P.R. China
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Published Online: 2017-06-26 | DOI: https://doi.org/10.1515/zna-2017-0137

Abstract

By using of the bilinear form, rational solutions and lump solutions of the potential Yu–Toda–Sasa–Fukuyama (YTSF) equation are derived. Dynamics of the fundamental lump solution, n1-order lump solutions, and N-lump solutions are studied for some special cases. We also find some interaction behaviours of solitary waves and one lump of rational solutions.

Keywords: Bilinear Form; Lump Solution; Potential YTSF Equation; Rational Solution

PACS: 02.30.Ik; 02.30.Jr

References

  • [1]

    S. J. Yu, K. Toda, N. Sasa, and T. Fukuyama, J. Phys. A Math. Gen. 31, 3337 (1998).Google Scholar

  • [2]

    C. L. Bai, X. Q. Liu, and H. Zhao, Commun. Theor. Phys. 42, 827 (2004).Google Scholar

  • [3]

    A. M. Wazwaz, Appl. Math. Comput. 203, 592 (2008).Google Scholar

  • [4]

    E. M. E. Zayed, J. Phys. A 42 (2009) 195202.Google Scholar

  • [5]

    H. O. Roshid, M. A. Akbar, M. N. Alam, M. F. Hoque, and N. Rahman, Springer Plus. 3, 122 (2014).Google Scholar

  • [6]

    C. L. Bai and H. Zhao, Chaos Solitons Fract. 27, 1026 (2006).Google Scholar

  • [7]

    A. Boz and A. Bekir, Comput. Math. Appl. 56, 1451 (2008).Google Scholar

  • [8]

    X. P. Zeng, Z. D. Dai, and D. L. Li, Chaos Solitons Fract. 42, 657 (2009).Google Scholar

  • [9]

    M. T. Darvishi and M. Najafi, Chin. Phys. Lett. 28, 040202 (2011).Google Scholar

  • [10]

    Z. T. Li and Z. D. Dai, Comput. Math Appl. 61, 1939 (2011).Google Scholar

  • [11]

    Y. J. Hu, H. L. Chen, and Z. D. Dai, Appl. Math. Comput. 234, 548 (2014).Google Scholar

  • [12]

    Z. Y. Yan, Phys. Lett. A. 318, 78 (2003).Google Scholar

  • [13]

    T. X. Zhang, H. N. Xuan, D. F. Zhang, and C. J. Wang, Chaos Solitons Fract. 34, 1006 (2007).Google Scholar

  • [14]

    H. L. Chen, Z. H. Xu, and Z. D. Dai, Abstr. Appl. Anal. 2014, 378167 (2014).Google Scholar

  • [15]

    Z. S. Lü and Y. N. Chen, Eur. Phys. J. B. 88, 187 (2015).CrossrefGoogle Scholar

  • [16]

    N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E. 80, 026601 (2009).Google Scholar

  • [17]

    P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, Eur. Phys. J. Special Topics. 185, 247 (2010).Google Scholar

  • [18]

    P. Dubard, and V. B. Matveev, Nat. Hazard. Earth Sys. Sci. 11, 667 (2011).Google Scholar

  • [19]

    B. L. Guo, L. M. Ling, and Q. P. Liu, Phys. Rev. E. 85, 026607 (2012).Google Scholar

  • [20]

    Y. Ohta and J. K. Yang, Proc. R. Soc. A Math. Phys. Eng. Sci. 468, 1716 (2011).Google Scholar

  • [21]

    Y. Ohta and J. K. Yang, Phys. Rev. E. 86, 036604. (2012).Google Scholar

  • [22]

    Y. Ohta and J. K. Yang, J. Phys. A 46, 105202 (2013).Google Scholar

  • [23]

    J. Satsuma and M. J. Ablowitz, J. Math. Phys. 20, 1496 (1979).Google Scholar

  • [24]

    Z. M. Lu, E. M. Tian, and R. Grimshaw, Wave Motion. 40, 123 (2004).Google Scholar

  • [25]

    J. H. Chang, arXiv: 1605.08966v1 (2016).Web of ScienceGoogle Scholar

  • [26]

    W. X. Ma, Phys. Lett. A. 379, 1975 (2015).Google Scholar

  • [27]

    J. Villarroel, J. Prada, and P. G. Estévez, Stud. Appl. Math. 122, 395 (2009).Google Scholar

  • [28]

    Q. L. Zha, Phys. Lett. A. 377, 3021 (2013).Google Scholar

  • [29]

    X. Lü and W. X. Ma, Nonlin. Dyn. 85, 1217 (2016).Google Scholar

  • [30]

    X. Lü, S. T. Chen, and W. X. Ma, Nonlinear Dyn. 86, 523 (2016).Google Scholar

  • [31]

    Y. B. Shi and Y. Zhang, Commun. Nonlinear Sci. Numer. Simul. 44, 120 (2017).Google Scholar

  • [32]

    R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge 2004.Google Scholar

About the article

Received: 2017-04-23

Accepted: 2017-05-25

Published Online: 2017-06-26

Published in Print: 2017-07-26


Citation Information: Zeitschrift für Naturforschung A, Volume 72, Issue 7, Pages 665–672, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2017-0137.

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