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Soliton-like solutions and chaotic motions for a forced and damped Zakharov–Kuznetsov equation in a magnetized electron–positron–ion plasma

Published online by Cambridge University Press:  29 July 2015

Hui-Ling Zhen ,
Bo Tian ,
De-Yin Liu ,
Lei Liu  and
Yan Jiang
Hui-Ling Zhen
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Bo Tian*
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
De-Yin Liu
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Lei Liu
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Yan Jiang
Affiliation:
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
*
†Email address for correspondence: [email protected]
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Abstract

A forced and damped Zakharov–Kuznetsov equation for a magnetized electron–positron–ion plasma affected by an external force is studied in this paper. Via the Hirota method, the soliton-like solutions are given. The soliton’s amplitude gets enhanced with the phase velocity ${\it\lambda}$ decreasing or ion-to-electron density ratio ${\it\beta}$ increasing. With the damped coefficient increasing, when the external force $g(t)$ is periodic, the two solitons are always parallel during the propagation and background of the two solitons drops on the $x{-}y$ plane, and amplitudes of the two solitons increase on the $x{-}t$ and $y{-}t$ planes, with $(x,y)$ as the coordinates of the propagation plane and $t$ as the time. When $g(t)$ is exponentially decreasing, the two solitons merge into a single one and the background rises on the $x{-}y$ plane, and amplitudes of the two solitons decrease on the $x{-}t$ and $y{-}t$ planes. Further, associated chaotic motions are obtained when $g(t)$ is periodic. Using the phase projections and Poincaré sections, we find that the chaotic motions can be weakened with ${\it\alpha}_{1}$ , the amplitude of $g(t)$ , decreasing. With ${\it\alpha}_{2}$ , the frequency of $g(t)$ , decreasing, a three-dimensional attractor with stretching-and-folding structure is found, indicating that the weak chaos is transformed into the developed chaos. Chaotic motions can also be weakened with ${\it\lambda}$ , the phase velocity, decreasing, but strengthened with ${\it\beta}$ , the ion-to-electron density ratio, and ${\it\alpha}_{2}$ decreasing.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 5 , October 2015 , 905810515
Copyright
© Cambridge University Press 2015 

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