扩展的非线性薛定谔方程中的孤子动力学
Soliton dynamics in an extended nonlinear Schrodinger equation with a spatial counterpart of the stimulated Raman scattering
摘要：
孤子的动力学被认为是在扩展的非线性薛定谔方程（NLSE）的框架，这是来自Zakharov的类型的高，低频率（HF和LF）波之间的相互作用的系统，其中的LF场受到扩散阻尼。该模型可用于HF波在等离子体中的传播。所得到的NLSE包括伪受激拉曼散射（PSRS）项，即，SRS项的空间域对应物，其作为光学中的时间域NLSE的成分而众所周知。还包括空间二阶衍射（SOD）的不均匀性。结果表明，由PSRS引起的孤子波数下移可以由SOD提供的波数上移补偿，SOD的系数是坐标的线性函数。得到了孤子的近似解析解。分析和数值结果吻合良好，包括PSRS和线性非均匀SOD之间的预测平衡。
英文摘要：
Dynamics of solitons is considered in the framework of the extended nonlinear Schrodinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves in plasmas. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (PSRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order diffraction (SOD). It is shown that the wavenumber downshift of solitons, caused by the PSRS, may be compensated by an upshift provided by the SOD whose coefficient is a linear function of the coordinate. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well, including the predicted balance between the PSRS and the linearly inhomogeneous SOD.
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