| 袁明生.非线性球形脉冲波在焦点的传播与干扰[J].,2016,56(2):176-180 |
| 非线性球形脉冲波在焦点的传播与干扰 |
| Propagation and interference of nonlinear spherical pulses at focus |
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| DOI：10.7511/dllgxb201602010 |
| 中文关键词: 一致 Lipschitz 球对称 几何光学 焦点 |
| 英文关键词: uniform Lipschitz spherical symmetry geometric optics focus |
| 基金项目:中央财政支持地方高校发展专项资金资助项目(YC-XK-13107). |
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| 中文摘要: |
| 在小初值的条件下，讨论了半线性波动方程组脉冲波解的性质，利用非线性几何光学的方法，证明非线性几何光学给出的解在焦点附近是有效的．描述了脉冲波的传播和干扰以及干扰后新脉冲波的产生情况．通过微分变换，利用球形对称性将波动方程组化为一阶双曲型方程，得到一阶近似解所满足的方程组．分析脉冲波在各个特征线方向的传播情况，得到近似解的一致有界性．对误差方程的解进行有效估计，得到近似解在焦点附近的较好的渐近性态． |
| 英文摘要: |
| The behavior of the pulses like solutions to a semilinear wave equations is discussed under small initial value conditions. Using the method of nonlinear geometric optics, it is proved that the solution obtained by using the nonlinear geometric optics is effective around the focus. The propagation and interference of pulses and the production of new pulses after the interference are stated. By making use of a differential transformation, the wave equations are translated into one-order hyperbolic ones because of the spherical symmetry, and the equations for the one-order approximate solutions are obtained accordingly. The propagation of the pulses along every different characteristic line is analyzed, and the uniform boundness for the approximate solutions is obtained. Finally, by effectively estimating the solutions for the error equations, the good asymptotic behavior of the approximate solutions is testified around the focus. |
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