Soliton solutions and chaotic motions for the (2+1)(2+1)-dimensional Zakharov equations in a laser-induced plasma

The (2+1)(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||E| is inversely related to ωpeωpe, but positively related to mimi and cscs, while nn is inversely related to ωpeωpe and ωLωL, but positively related to n0n0, with EE as the envelope of the high-frequency electric field, nn as the plasma density, while ωpeωpe, ωLωL, n0n0, mimi and cscs 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 ωpeωpe increasing or n0n0 decreasing. Also, period of the bound-state interaction decreases with ωLωL decreasing. Considering the driving forces in the laser-induced plasma, we explore the associated chaotic motions as well as the effects of ωLωL, ωpeωpe, kLkL, n0n0, mimi, cscs, ωF1ωF1 and ωF2ωF2, where kLkL is the wave number of the laser beam, ωF1ωF1 and ωF1ωF1 represent the frequencies of driving forces, respectively. It is found that the chaotic motions can be weakened with ωpeωpe, cscs and ωF1ωF1 increasing, or with n0n0, mimi and ωF2ωF2 decreasing, and the periodic motion can occur when ωF1ωF1 reaches the critical value 2π2π, while the chaotic motions are independent of ωLωL and kLkL.