Han Seung-Ho, Park Q-Han
Nano Optical Property Laboratory and Department of Physics, Kyung Hee University, Seoul 130-701, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066601. doi: 10.1103/PhysRevE.83.066601. Epub 2011 Jun 7.
We present an analytic method to generate solutions for the optical fiber soliton system that reveals self-steepening effects on solitons coupled to a continuous wave. Exact soliton solutions are obtained by adopting a universal Lax pair technique that solves simultaneously the nonlinear Schrödinger (NLS) equation and the derivative NLS equation. We find that, in the presence of a self-steepening term, the bright type NLS equation with abnormal group velocity dispersion is related to the dark type NLS equation with normal group velocity dispersion and, accordingly, exact soliton solutions of the bright type NLS equation describe both bright and dark solitons depending on the strength of the continuous wave. The self-steepening effect on solitons and possible applications of a continuous wave for the control of solitons are explained.
我们提出了一种解析方法来生成光纤孤子系统的解，该方法揭示了耦合到连续波的孤子上的自陡峭效应。通过采用一种通用的拉克斯对技术获得精确的孤子解，该技术同时求解非线性薛定谔（NLS）方程和导数NLS方程。我们发现，在存在自陡峭项的情况下，具有反常群速度色散的亮型NLS方程与具有正常群速度色散的暗型NLS方程相关，因此，亮型NLS方程的精确孤子解根据连续波的强度描述亮孤子和暗孤子。解释了对孤子的自陡峭效应以及连续波在孤子控制方面的可能应用。
