Soliton solutions and chaotic motions for the [formula omitted]-dimensional Zakharov equations in a laser-induced plasma

Abstract

The (2+1)-dimensional Zakharov equations arising from the propagation of a laser beam in a plasma are studied in this paper. Analytic soliton solutions are obtained by means of the symbolic computation, based on which we find that |E| is inversely related to ωpe, but positively related to mi and cs, while n is inversely related to ωpe and ωL, but positively related to n0, with E as the envelope of the high-frequency electric field, n as the plasma density, while ωpe, ωL, n0, mi and cs as the plasma electronic frequency, frequency of the laser beam, mean density of the plasma, mass of an ion and ion-sound velocity in the plasma, respectively. Head-on interaction is found to be transformed into an overtaking one with ωpe increasing or n0 decreasing. Also, period of the bound-state interaction decreases with ωL decreasing. Considering the driving forces in the laser-induced plasma, we explore the associated chaotic motions as well as the effects of ωL, ωpe, kL, n0, mi, cs, ωF1 and ωF2, where kL is the wave number of the laser beam, ωF1 and ωF1 represent the frequencies of driving forces, respectively. It is found that the chaotic motions can be weakened with ωpe, cs and ωF1 increasing, or with n0, mi and ωF2 decreasing, and the periodic motion can occur when ωF1 reaches the critical value 2π, while the chaotic motions are independent of ωL and kL.