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

摘要

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 lambda decreasing or ion-to-electron density ratio 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 Poincare sections, we find that the chaotic motions can be weakened with alpha(1), the amplitude of g(t), decreasing. With 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 lambda, the phase velocity, decreasing, but strengthened with beta, the ion-to-electron density ratio, and alpha(2) decreasing.