光学学报, 2010, 30 (10): 3000, 网络出版: 2012-10-24
向列相液晶中的(1+1)维呼吸子解
(1+1)-D Breathers Solution in Nematic Liquid Crystals
向列相液晶 非局域程度 非线性 薛定谔方程 呼吸子 nematic liquid crystal degree of nonlocality nonlinearity Schrdinger equation breathers
摘要
理论分析了(1+1)维呼吸子在向列相液晶中传输时的情况,通过对原始方程作归一化计算和相应的傅里叶变换,得到了特定情况下的强非局域非线性薛定谔方程,并且通过此方程最终求到了呼吸子解。在未作近似时可以计算出呼吸子的周期和最大(最小)束宽,在平衡点处将势函数近似展开到二阶,此时不仅得出了呼吸子解的周期和最大(最小)束宽,而且解出了波动振幅的解析解。通过数值模拟与解析解的比较,结果表明,解析结果成立于非局域程度较强的情况,并且未作近似的解析解始终比较接近模拟解。
Abstract
The evolution of (1+1)-D breathers in nonlocal nonlinear media is theoretically discussed, and it is modeled by the nonlocal nonlinear Schrdinger equation (NNLSE) which is got from the normalized equations and corresponding Fourier transform. In the balance, the potenfial is approximate to the 2nd order, a fundamental breathers solution is presented, and the solutions of the period and the maximal (minimal) beam width is obtained too. Without approximation, precise solutions of the period and the maximal (minimal) beam widths are also calculated here. Compared with the numerical simulations, it is obviously found that the analytical solutions are suitable in the strongly nonlocal case and the breathers solution in the 2nd approximation is always less accurate than that with no apptoximation.
朱叶青, 胡巍, 曹龙贵. 向列相液晶中的(1+1)维呼吸子解[J]. 光学学报, 2010, 30(10): 3000. Zhu Yeqing, Hu Wei, Cao Longgui. (1+1)-D Breathers Solution in Nematic Liquid Crystals[J]. Acta Optica Sinica, 2010, 30(10): 3000.