Soliton evolution and radiation loss for the nonlinear Schrödinger equation.
Soliton evolution and radiation loss for the nonlinear Schrödinger equation.
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非线性薛定谔方程的孤子演化和辐射损耗。
DOI：
10.1103/physreve.51.1484
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
Noel F. Smyth
中科院分区：
文献类型：
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作者：
W. Kath;Noel F. Smyth
研究了非线性Schrödinger （NLS）方程一般初始脉冲向孤子的瞬态演化。利用一个由可变参数的类孤子脉冲加上平均拉格朗日中的线性色散项组成的试函数，推导出近似这种演化的常微分方程（ODE）。这些近似方程考虑了所产生的色散辐射对脉冲演化的影响。具体地说，在近似的ODE中，辐射起到阻尼的作用，使脉冲衰减为稳定的孤子。将近似ODE的解与NLS方程的数值解进行了比较，发现两者吻合得很好。此外，本文还讨论了在光纤和其他由nls型方程（如孤子逻辑门）控制的器件中获得孤子传播的改进近似ODE模型的潜在意义。
The transient evolution of general initial pulses into solitons for the nonlinear Schrödinger (NLS) equation is considered. By employing a trial function which consists of a solitonlike pulse with variable parameters plus a linear dispersive term in an averaged Lagrangian, ordinary differential equations (ODE’s) are derived which approximate this evolution. These approximate equations take into account the effect of the generated dispersive radiation upon the pulse evolution. Specifically, in the approximate ODE’s the radiation acts as a damping which causes the pulse to decay to a steady soliton. The solutions of the approximate ODE’s are compared with numerical solutions of the NLS equation and are found to be in very good agreement. In addition, the potential implications for obtaining improved approximate ODE models for soliton propagation in optical fibers and other devices governed by NLS-type equations, such as soliton logic gates, are discussed.