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

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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.

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Acknowledgements

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

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  1. Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China

    Xi-Yang Xie & Gao-Qing Meng

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  1. Xi-Yang Xie
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  2. Gao-Qing Meng
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Correspondence to Xi-Yang Xie.

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Xie, XY., Meng, GQ. Dark solitons for the (2+1)-dimensional Davey–Stewartson-like equations in the electrostatic wave packets. Nonlinear Dyn 93, 779–783 (2018). https://doi.org/10.1007/s11071-018-4226-x

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  • DOI: https://doi.org/10.1007/s11071-018-4226-x

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