变色散系数的非线性色谱方程

由物理化学导出了一个变色散系数的非线性色谱方程，给出了它与线性色谱方程之间的联系及它的自－Ｂａｃｋｌｕｎｄ变换．证明了非线性色谱方程的初值问题和半直线（ｘ≥０）上的（线性和非线性）边值一初值问题的解可借助线性色谱方程相应的线性问题的解去构造．

变系数五阶色散方程的精确解

运用李群分析对变系数五阶色散方程求出李点对称,对变系数的存在性进行讨论,可以得到不同的向量场.进一步约化成常微分方程,利用指数展开法、e-(x)展开法和幂级数展开法求出变系数五阶色散方程的精确解.最后,给出变系数五阶色散方程的守恒律.

分离变量法在变系数(2+1)维方程求解中的应用

分离变量法是求解具有局域相干结构解的有效解析方法.考虑到传播介质的非均匀性和边界的不一致性,变系数(2+1)色散长波方程可以实际地描述宽广的河道或有限深的远海中非线性波的传播.解析研究了变系数(2+1)维色散长波方程.通过分离变量法,得到了该方程组的具有丰富结构的分离变量解.

(G′/G)展开法与高维非线性物理方程的新分形结构

将(G′/G)展开法扩展到研究高维非线性物理方程的非行波解和分形结构.以(2+1)维变系数色散长波系统为例,构造出该系统的非行波解,对解中的任意函数进行适当的设置,发现了一类新的分形结构,即十字形分形结构.

Effects Of Average Index Variation in Apodized Long-Period Fiber Gratings

We analyze the effects of average index variation on the transmission characteristics of an index-apodized long-period fiber grating （LPFG） by the transfer matrix method and study how these effects depend on the grating length, the grating profile, the modal dispersion factor, and the duty cycle of the index modulation. Apart from shifting the resonance wavelength and modifying the rejection band, average index variation can give rise to significant side lobes that may appear on the short-wavelength or long-wavelength side of the rejection band, depending on the signs of the average index change and the modal dispersion factor. Our results provide general guidance for the writing of LPFGs for the minimization of side lobes. Our analysis compares well with published experimental results and should be useful for the design and fabrication of LPFGs.