摘要
近年来,用光孤子传输信息的光纤通信系统在长距离、大容量传输方面凸显了自身的优势,必将在新一代通信技术与商用上发挥巨大的作用。光孤子在光纤中的传输满足非线性薛定谔方程。从寻求行波变换、求解过程和解的物理意义等方面,对于求解非线性薛定谔方程常用的三种求解方法即Jacobi椭圆函数展开法、三角函数假设法和试探函数法进行了分析整理及优劣比较,并引入了新近提出的(G′/G)展开法。计算表明,(G′/G)展开法在行波变换和计算过程都相对其他三种方法简单,且得到的解也较为丰富,因此,该展开法在非线性薛定谔方程及相关方程的求解中具有广阔的应用前景。
In recent years, the fiber optical communication system that uses optical soliton to transmit information has shown its advantages in long transmission distance and large capacity. It will play a great role in the new generation of communication and business. The transmission of optical soliton in optical fiber obeys the nonlinear Schr.dinger equation. In this paper, three commonly used methods for solving nonlinear Schr.dinger equation, i.e., Jacobi elliptic function expansion method, trigonometric function assumption, and trial function method, are analyzed and compared from the aspects of seeking traveling wave transformation, solving process and physical significance of solution, and so on. Moreover, we introduce the newly proposed （G′/G） expansion method. Calculation shows that （G′/G） expansion method is easier than the other three methods in traveling wave transformation and calculation process. Besides, it also has relatively rich solutions. Therefore, this expansion method solving the nonlinear Schr.dinger equation and the related equations has a wide application prospect.
出处
《激光与光电子学进展》
CSCD
北大核心
2014年第4期57-62,共6页
Laser & Optoelectronics Progress
基金
国家自然科学基金(11071159)
内蒙古自然科学基金(2010MS0115)
