柱面非线性麦克斯韦方程组的行波解

发布时间：2018-02-14 01:30

本文关键词： 柱面电磁波非线性介质行波解自陡　出处：《物理学报》2017年13期 　论文类型：期刊论文

【摘要】：柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.
[Abstract]:The problem of cylindrical electromagnetic wave propagation in a variety of non-uniform nonlinear media is of great value. The cylindrical nonlinear Maxwell equations describing the problem are solved accurately. But due to the extreme complexity of nonlinear partial differential equations, it is very difficult to solve the arbitrary initial boundary value conditions objectively. Previous work has only solved the propagation of cylindrical electromagnetic waves in non-dispersive media with exponential nonlinear factors. Therefore, for more definite physical scenarios, solutions that can accurately describe the broader physical properties are sought. In this paper, we discuss the exact solutions of the cylindrical Maxwell equations in nondispersive media with arbitrary nonlinear factors and power law inhomogeneous factors. Theoretical analysis shows that in this case, the electric field component E of the cylindrical electromagnetic wave no longer exists a plane traveling wave solution, which is usually shaped as E _ G _ r ~ (-kt), and then the corresponding nonlinear ordinary differential equations are replaced and solved by appropriate variables. The generalized traveling wave solution in the form of electric field component EG Gnn r-kt) is given, and the physical phenomenon similar to the self-steepening effect in the solution is illustrated by an example.
【作者单位】：四川大学数学学院;
【分类号】：O411

【相似文献】