Advertisement

Nonlinear Dynamics

, Volume 93, Issue 2, pp 779–783 | Cite as

Dark solitons for the (2+1)-dimensional Davey–Stewartson-like equations in the electrostatic wave packets

Original Paper
  • 150 Downloads

Abstract

Under investigation in this paper are the (2+1)-dimensional Davey–Stewartson-like equations, which can be used to describe the slow modulation of (2+1)-dimensional electrostatic wave packets in the ultra-relativistic degenerate dense plasmas. With figures plotted, stable propagation of the one solitons and elastic collisions between the two solitons are, respectively, analyzed. Moreover, influences of the parameters \(\chi _{1}\) and \(\chi _{5}\) on the dark solitons are illustrated in detail, where \(\chi _{1}\) arises because of the evolution of the electrostatic wave packets and wave group dispersion, and \(\chi _{5}\) rests with the zeroth harmonic static field of the plasmas: Widths of the solitons become narrower with the value of \(\chi _{1}\) increasing; meanwhile, amplitudes of the one solitons become lower and velocities of the two solitons alter. With the decrease of \(\chi _{5}\), amplitudes become lower for the one solitons but higher for the two solitons.

Keywords

Davey–Stewartson-like equations Symbolic computation Dark-soliton solutions Elastic collisions 

Notes

Acknowledgements

This work has been supported by the Fundamental Research Funds for the Central Universities (No. 2018MS132).

Compliance with ethical standards

Conflict of interest

The author declare that there is no conflict of interest regarding the publication of this paper.

References

  1. 1.
    Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nat. Photon. 8, 755–764 (2014)CrossRefGoogle Scholar
  2. 2.
    Abida, M., Huepeb, C., Metensc, S., Nored, C., Phame, C.T., Tuckermand, L.S., Brachete, M.E.: Gross-Pitaevskii dynamics of Bose-Einstein condensates and superfluid turbulence. Fluid Dyn. Res. 33, 509–544 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Pandey, B.P., Vladimirov, S.V., Samarian, A.: Nonlinear waves in collisional dusty plasma. Phys. Plasmas 15, 053705 (2008)CrossRefGoogle Scholar
  4. 4.
    Sun, W.R., Liu, D.Y., Xie, X.Y.: Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrodinger equations in the birefringent optical fibers. Chaos 27, 043114 (2017)CrossRefMATHGoogle Scholar
  5. 5.
    Liu, C., Yang, Z.Y., Zhao, L.C., Yang, W.L.: State transition induced by higher-order effects and background frequency. Phys. Rev. E 91, 022904 (2015)CrossRefGoogle Scholar
  6. 6.
    Wang, L., Zhu, Y.J., Qi, F.H., Li, M., Guo, R.: Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers. Chaos 25, 063111 (2015)MathSciNetCrossRefGoogle Scholar
  7. 4.
    Agrawal, G.P.: Nonlinear Fiber Optics. Acad, San Diego (2001)MATHGoogle Scholar
  8. 5.
    Davey, A., Stewartson, K.: On three-dimensional packets of surface waves. Proc. R. Soc. Lond. Ser. A 338, 101–110 (1974)MathSciNetCrossRefMATHGoogle Scholar
  9. 6.
    Kivshar, Y.S., Luther-Davies, B.: Dark optical solitons: physics and applications. Phys. Rep. 298, 81–197 (1998)CrossRefGoogle Scholar
  10. 7.
    Królikowski, W., Akhmediev, N., Luther-Davies, B.: Dark solitons with total phase shift greater than pi. Phys. Rev. E 48, 3980–3987 (1993)CrossRefGoogle Scholar
  11. 8.
    Zhao, W., Bourkoff, E.: Propagation properties of dark solitons. Opt. Lett. 14, 703–705 (1989)CrossRefGoogle Scholar
  12. 9.
    Gen, D.P., Pu, F.C., Zhao, B.H.: Exact solution for quantum Davey–Stewartson. Phys. Rev. Lett. 65, 3227–3229 (1990)MathSciNetCrossRefMATHGoogle Scholar
  13. 10.
    Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. Appl. Phys. Lett. 23, 142–144 (1973)CrossRefGoogle Scholar
  14. 11.
    Haus, H.A., Wong, W.S.: Solitons in optical communications. Rev. Mod. Phys. 68, 423–444 (1996)CrossRefGoogle Scholar
  15. 12.
    Wu, Y., Deng, L.: Ultraslow optical solitons in a cold four-state medium. Phys. Rev. Lett. 93, 1439041 (2004)Google Scholar
  16. 13.
    Misra, A.P., Shukla, P.K.: Stability and evolution of wave packets in strongly coupled degenerate plasmas. Phys. Rev. E 85, 026409 (2012)CrossRefGoogle Scholar
  17. 14.
    Misra, A.P., Shukla, P.K.: Modulational instability and nonlinear evolution of two-dimensional electrostatic wave packets in ultra-relativistic degenerate dense plasmas. Phys. Plasmas 18, 042308 (2011)CrossRefGoogle Scholar
  18. 15.
    Huang, G., Deng, L., Hang, C.: Davey-Stewartson description of two-dimensional nonlinear excitations in Bose–Einstein condensates. Phys. Rev. E 72, 036621 (2005)CrossRefGoogle Scholar
  19. 16.
    Skupin, S., Bang, O., Edmundson, D., Krolikowski, W.: Stability of two-dimensional spatial solitons in nonlocal nonlinear media. Phys. Rev. E 73, 066603 (2006)CrossRefGoogle Scholar
  20. 17.
    Zhou, H.P., Tian, B., Mo, H.X., Li, M., Wang, P.: Bäcklund transformation, Lax pair and solitons of the (2+1)-dimensional Davey–Stewartson like equations with variable coefficients for the electrostatic wave packets. J. Nonlinear Math. Phys. 20, 94–105 (2013)MathSciNetCrossRefGoogle Scholar
  21. 18.
    Hirota, R.: The Direct Method in Soliton Theory. Cambridge Univ. Press, Cambridge (2004)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsNorth China Electric Power UniversityBaodingChina

Personalised recommendations