Conservation Laws in Higher-Order Nonlinear Optical Effects
摘要
Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schr\"{o}dinger equation. The first few currents and charges are also presented explicitly. Due to the higher-order effects, conservation laws of the nonlinear Schr\"{o}dinger equation are violated in general. The differences between the types of the conserved currents for the Hirota and the Sasa-Satsuma equations imply that the higher-order terms determine the inherent types of conserved quantities for each integrable cases of the higher-order nonlinear Schr\"{o}dinger equation.
引用
@article{arxiv.solv-int/9904008,
title = {Conservation Laws in Higher-Order Nonlinear Optical Effects},
author = {Jongbae Kim and Q-Han Park and H. J. Shin},
journal= {arXiv preprint arXiv:solv-int/9904008},
year = {2009}
}