In this paper, we study the higher-order generalized nonlinear Schrödinger equation describing the propagation of ultrashort optical pulse in optical fibers. The Hirota’s bilinear method is employed to succinctly derive one-soliton and two-soliton solutions of the equation. Furthermore, the main characteristics of these solutions are graphically demonstrated. In particular, the influences of each parameters on period interactions between solitons are discussed in detail, and the approach of how to control the cycle of interactions is analyzed.

中文翻译：

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具有高阶效应的非线性系统中的孤子

在本文中，我们研究了描述超短光脉冲在光纤中传播的高阶广义非线性Schrödinger方程。采用Hirota的双线性方法简洁导出方程的一孤子和二孤子解。此外，这些解决方案的主要特征以图形方式展示。特别地，详细讨论了每个参数对孤子之间的周期相互作用的影响，并分析了如何控制相互作用周期的方法。