Solitons and chaos of the Klein-Gordon-Zakharov system in a high-frequency plasma

Abstract

In this paper, we study the Klein-Gordon-Zakharov (KGZ) system, which describes the interaction between the Langmuir wave and ion sound wave in a high-frequency plasma. By means of the Hirota method and symbolic computation, bright and mixed-type soliton solutions are obtained. For the one soliton, amplitude of E is positively related to β2, and that of n is inversely related to β2, while they are both positively related to α, where E refers to the high-frequency part of the electrostatic potential of the electric field raised by the electrons, and n represents the deviation of ion density from its equilibrium, β2 and α are the plasma frequency and ion sound speed, respectively. Head-on interactions between the two bright solitons and two mixed-type ones are respectively displayed. With β2 increasing, the head-on interaction is transformed into an overtaking one. Bright bound-state solitons are investigated, and the interaction period decreases with α increasing. Furthermore, with the external forces Γ1(t) and Γ2(t) introduced, the perturbed KGZ system is studied numerically for its associated chaotic motions. Both the weak and developed chaotic motions can be observed. Γ1(t) and Γ2(t) have different effects on the chaotic motions: the chaotic motion can be weakened by decreasing the amplitude of Γ1(t) or increasing the amplitude and frequency of Γ2(t).