Mixed-type soliton solutions for the -coupled Hirota system in an optical fiber

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• 作者：Lei Liu ; Bo Tian ; ^{tian_bupt@163.com" class="auth_mail" title="E-mail the corresponding author} ; Wen-Rong Sun ; Xiao-Yu Wu
• 关键词：NN-coupled Hirota system ; Mixed-type soliton solutions ; Symbolic computation ; Improved bilinear forms ; Optical fiber
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：72
• 期：4
• 页码：807-819
• 全文大小：1655 K

文摘

Under investigation in this paper is the N$N$-coupled Hirota system which describes the ultrashort pulse simultaneous propagation of the N$N$-field components in an optical fiber. Through the Hirota method and symbolic computation, using some auxiliary functions, we obtain the improved bilinear forms and two mixed-type soliton solutions for the 3$3$-coupled Hirota system, while the system admits two mixed-type solitons for all the cases of σ₁${\sigma }_1$, σ₂${\sigma }_2$ and σ₃${\sigma }_3$, which the represent the defocusing or focusing nonlinearities of the 3$3$ components. With the help the analytic and graphic analysis, we study the properties and interactions for the two mixed-type solitons for the 3$3$-coupled Hirota system. Amplitudes for the two mixed-type one solitons are not affected by γ$\gamma$, but their velocities are linearly related to γ$\gamma$, with γ$\gamma$ as the higher-order effect which represents the relative width of the spectrum that arises due to the quasi-monochromocity. For the 2-bright-1-dark two solitons, there exist the elastic and inelastic interactions, while for the 1-bright-2-dark two solitons, there is only the elastic interaction. The 2-bright-1-dark and 1-bright-2-dark bound-state two solitons are also presented. Finally, we extend those results to the N$N$-coupled Hirota system.