非Kerr光纤中亮孤子的稳定性与相互作用
Stability and interaction of bright solitons in non-Kerr fiber
胡唯伊 1王运涛 2徐友才 3张世全1
作者信息
- 1. 四川大学数学学院,成都 610064
- 2. 天府工程数值模拟与软件工程创新中心,成都 610207
- 3. 四川大学数学学院,成都 610064;天府工程数值模拟与软件工程创新中心,成都 610207
- 折叠
摘要
非Kerr光纤中的亮孤子的演化可以用具有三次-五次竞争非线性项的非线性薛定谔方程来描述.为数值求解该方程的初值问题,本文将无界区域截断为有界区域,根据亮孤子在远场的渐近行为构造了合理的边界条件,从而将该初值问题转换为初边值问题.对这个初边值问题,本文分别提出 了 Crank-Nicolson 有限差分(Crank-Nicolson Finite Difference,CNFD)格式和时间分裂有限差分(Time-Splitting Finite Difference,TSFD)格式.这两种格式在空间和时间维度上都具有二阶精度,其中CNFD格式是全隐格式,可以守恒离散能量和质量,TSFD是线性隐式格式,可以守恒离散质量.在以数值算例验证两种方法的计算效率后,本文用TSFD格式研究了非Kerr光纤中亮孤子的稳定性与相互作用.
Abstract
Dynamical behaviors of bright solitons can be described by the nonlinear Schrödinger equation(NLSE)with cubic-quintic competing nonlinear terms.In this paper,to numerically solve the initial val-ue problem of the NLSE,two difference schemes are proposed.Firstly,we transfer the initial value problem into the initial value problem with boundary conditions,truncate the unbounded region into a bounded region and constructe a reasonable boundary condition based on the asymptotic behaviors of bright solitons in the far field.Then we design the Crank-Nicolson finite difference(CNFD)and time-splitting finite difference(TSFD).The CNFD scheme is fully implicit and can conserve discrete energy and mass.Meanwhile,the TSFD scheme is linear implicit and can only conserve discrete mass.Finally,after the performance of the two schemes is compared by some examples,we explore the stability and in-teraction of bright solitons by using the TSFD scheme.
关键词
亮孤子/薛定谔方程/三次-五次非线性/非Kerr光纤Key words
Bright soliton/Schrödinger equation/Cubic-quintic nonlinearity/Non-Kerr fiber引用本文复制引用
基金项目
国家重大专项(GJXM92579)
四川省自然科学基金(2023NSFSC0075)
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据