Karpman VI
Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Oct;62(4 Pt B):5678-87. doi: 10.1103/physreve.62.5678.
The resonant radiation of solitons due to higher order dispersion, described by an extended nonlinear Schrodinger (NLS) equation with nonlinear (cubic) dispersive terms and linear terms with third and fourth derivatives, is studied. The basic equation includes, as a particular case, a higher order derivative NLS equation. General properties of the master equation, such as conservation laws, Hamiltonian structures (in important particular cases), and Galilei transformation are studied. Explicit asymptotic expressions, describing the radiation at different initial conditions, are derived. The obtained results, in particular, provide a basis for the study of soliton losses, caused by the radiation, in optical fibers.
研究了由具有非线性（立方）色散项以及三阶和四阶导数线性项的扩展非线性薛定谔（NLS）方程所描述的、由于高阶色散导致的孤子共振辐射。作为一个特殊情况，基本方程包含一个高阶导数NLS方程。研究了主方程的一般性质，如守恒律、哈密顿结构（在重要的特殊情况下）以及伽利略变换。推导了描述不同初始条件下辐射的显式渐近表达式。所获得的结果尤其为研究光纤中由辐射引起的孤子损耗提供了基础。
