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

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.