Skip to main content
SpringerLink
Log in

Bright and dark N-soliton solutions for the (2 + 1)-dimensional Maccari system

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

Under investigation in this paper is the (2 + 1) -dimensional Maccari system, which is related to the Kadomtsev-Petviashvili (KP) equation. Bright and dark N -soliton solutions in terms of the Gramian are obtained via the KP hierarchy reduction. Oblique and parallel interactions between the bright solitons and between the dark solitons are studied analytically and graphically. We find that there are elastic and inelastic interactions for the bright solitons, but there are only elastic interactions for the dark solitons. Resonance, breather, attraction and repulsion structures are presented. It is expected that these soliton interactions have potential applications in fluid dynamics, nonlinear optics and plasma physics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, New York, 2007)

  2. M.J. Ablowitz, P.A. Clarkson, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1991)

  3. L. Wang, J.H. Zhang, C. Liu, M. Li, F.H. Qi, Phys. Rev. E 93, 062217 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  4. L. Wang, Y.J. Zhu, F.H. Qi, M. Li, R. Guo, Chaos 25, 063111 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  5. N.J. Zabusky, M.D. Kruskal, Phys. Rev. Lett. 15, 240 (1965)

    Article  ADS  Google Scholar 

  6. B.B. Kadomtsev, V.I. Petviashvili, Sov. Phys. Dokl. 15, 539 (1970)

    ADS  Google Scholar 

  7. M. Ablowitz, Nonlinear Dispersive Waves, Asymptotic Analysis and Solitons (Cambridge University Press, Cambridge, 2011)

  8. L. Wang, J.H. Zhang, Z.Q. Wang, C. Liu, M. Li, F.H. Qi, R. Guo, Phys. Rev. E 93, 012214 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  9. L. Wang, Y.J. Zhu, Z.Q. Wang, T. Xu, F.H. Qi, Y.S. Xu, J. Phys. Soc. Jpn. 85, 024001 (2016)

    Article  ADS  Google Scholar 

  10. X.Y. Tang, S.Y. Lou, Y. Zhang, Phys. Rev. E 66, 1 (2002)

    Article  Google Scholar 

  11. X.Y. Tang, J.M. Li, S.Y. Lou, Phys. Scr. 75, 201 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Boiti, L. Martina, O.K. Pashaev, F. Pempinelli, Phys. Lett. A 160, 55 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  13. R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press, Cambridge, 2004)

  14. V.B. Matveev, M.A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1991)

  15. M.J. Ablowitz, H. Segur, J. Fluid Mech. 92, 691 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  16. M.J. Ablowitz, D.E. Baldwin, Phys. Rev. E 86, 036305 (2012)

    Article  ADS  Google Scholar 

  17. A. Maccari, J. Math. Phys. 37, 6207 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  18. K. Porsezian, J. Math. Phys. 38, 4675 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  19. H. Zhao, Chaos, Solitons Fractals 36, 359 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  20. C. Ye, W. Zhang, Chaos, Solitons Fractals 44, 1063 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  21. N. Cheemaa, M. Younis, Nonlinear Dyn. 83, 1395 (2016)

    Article  Google Scholar 

  22. H.L. Zhen, B. Tian, W.R. Sun, Appl. Math. Lett. 27, 90 (2014)

    Article  MathSciNet  Google Scholar 

  23. G.F. Yu, Z.W. Xu, Phys. Rev. E 91, 062902 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  24. C.Q. Dai, Y.Y. Wang, Indian J. Phys. 87, 679 (2013)

    Article  ADS  Google Scholar 

  25. C. Wang, Z. Dai, C. Liu, Adv. Math. Phys. 2015, 861069 (2015)

    Google Scholar 

  26. G.H. Wang, L.H. Wang, J.G. Rao, J.S. He, Commun. Theor. Phys. 67, 601 (2017)

    Article  ADS  Google Scholar 

  27. M. Jimbo, T. Miwa, Publ. RIMS 19, 943 (1983)

    Article  Google Scholar 

  28. C. Gilson, J. Hietarinta, J. Nimmo, Y. Ohta, Phys. Rev. E 68, 016614 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  29. Y. Ohta, AIP Conf. Proc. 1212, 114 (2010)

    Article  ADS  Google Scholar 

  30. Y. Ohta, D.S. Wang, J. Yang, Stud. Appl. Math. 127, 345 (2011)

    Article  MathSciNet  Google Scholar 

  31. Y. Ohta, J. Yang, Proc. R. Soc. A 468, 1716 (2012)

    Article  ADS  Google Scholar 

  32. B.F. Feng, J. Phys. A 47, 355203 (2014)

    Article  MathSciNet  Google Scholar 

  33. J. Chen, Y. Chen, B.F. Feng, K. Maruno, J. Phys. Soc. Jpn. 84, 074001 (2015)

    Article  ADS  Google Scholar 

  34. J. Chen, Y. Chen, B.F. Feng, K. Maruno, Phys. Lett. A 379, 1510 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  35. J.W. Yang, Y.T. Gao, C.Q. Su, C. Zhao, Y.J. Feng, Comput. Math. Appl. 72, 2685 (2016)

    Article  MathSciNet  Google Scholar 

  36. J.W. Yang, Y.T. Gao, Y.H. Sun, Y.J. Shen, C.Q. Su, Eur. Phys. J. Plus 131, 416 (2016)

    Article  Google Scholar 

  37. G. Mu, Z. Qin, Nonlinear Anal. 18, 1 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China

    Lei Liu, Bo Tian, Yu-Qiang Yuan & Yan Sun

Authors
  1. Lei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu-Qiang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bo Tian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, L., Tian, B., Yuan, YQ. et al. Bright and dark N-soliton solutions for the (2 + 1)-dimensional Maccari system. Eur. Phys. J. Plus 133, 72 (2018). https://doi.org/10.1140/epjp/i2018-11880-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2018-11880-8

Search

Navigation