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

  • Xi-Yang Xie
  • Gao-Qing Meng
Original Paper


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.


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



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.


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© 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

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