The exact solutions to dispersive long-wave equations are obtained by a polynomial expansion method based on the idea of the homogeneous balance method.
基于齐次平衡法的思想，利用多项式展开法解得了具有色散项的长波方程组的精确解。
The Gaussian index profile of a diffused optical waveguide is approximated by an appropriate polynomial, and the asymptotic solutions of the mode efficient index is derived in a analytical form.
本文用适当的多项式函数近似扩散光波导的高斯折射率分布函数，推导了导模有效折射率的解析形式渐近解。
Moreover, we investigate the existence of analytic solutions for polynomial-like iterative equations with variable coefficients and improve some known results.
同时也研究了变系数多项式型迭代函数方程解析解的存在性，其结果改进和推广了作者本人以前的工作。
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