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

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• 作者：Hui-Ling Zhen ; Bo Tian ; ^{tian_bupt@163.com" class="auth_mail" title="E-mail the corresponding author} ; Ya Sun ; Jun Chai
• 关键词：Laser-induced plasma ; (2+1)(2+1)-dimensional Zakharov equations ; Soliton interaction ; Chaotic motions ; Symbolic computation
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：71
• 期：7
• 页码：1337-1348
• 全文大小：4631 K

文摘

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|$\left|E\right|$ is inversely related to ω_pe${\omega }_{pe}$, but positively related to m_i$m_i$ and c_s$c_s$, while n$n$ is inversely related to ω_pe${\omega }_{pe}$ and ω_L${\omega }_L$, but positively related to n₀$n_0$, with E$E$ as the envelope of the high-frequency electric field, n$n$ as the plasma density, while ω_pe${\omega }_{pe}$, ω_L${\omega }_L$, n₀$n_0$, m_i$m_i$ and c_s$c_s$ 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 ω_pe${\omega }_{pe}$ increasing or n₀$n_0$ decreasing. Also, period of the bound-state interaction decreases with ω_L${\omega }_L$ decreasing. Considering the driving forces in the laser-induced plasma, we explore the associated chaotic motions as well as the effects of ω_L${\omega }_L$, ω_pe${\omega }_{pe}$, c273c20477183b27866d4ac6f398" title="Click to view the MathML source">k_L$k_L$, n₀$n_0$, m_i$m_i$, c_s$c_s$, 37c93fd4764b87183009e5e" title="Click to view the MathML source">ω_F1${\omega }_{F_1}$ and ω_F2${\omega }_{F_2}$, where c273c20477183b27866d4ac6f398" title="Click to view the MathML source">k_L$k_L$ is the wave number of the laser beam, 37c93fd4764b87183009e5e" title="Click to view the MathML source">ω_F1${\omega }_{F_1}$ and 37c93fd4764b87183009e5e" title="Click to view the MathML source">ω_F1${\omega }_{F_1}$ represent the frequencies of driving forces, respectively. It is found that the chaotic motions can be weakened with ω_pe${\omega }_{pe}$, c_s$c_s$ and 37c93fd4764b87183009e5e" title="Click to view the MathML source">ω_F1${\omega }_{F_1}$ increasing, or with n₀$n_0$, m_i$m_i$ and ω_F2${\omega }_{F_2}$ decreasing, and the periodic motion can occur when 37c93fd4764b87183009e5e" title="Click to view the MathML source">ω_F1${\omega }_{F_1}$ reaches the critical value 2π$2\pi$, while the chaotic motions are independent of ω_L${\omega }_L$ and c273c20477183b27866d4ac6f398" title="Click to view the MathML source">k_L$k_L$.