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1·In this paper, we discuss the locally topological structures of nonlinear homogeneous systems with one zero characteristic root, and give a criteria by the right-hand polynomial coefficients.

本文讨论了具有一个零特征根的非线性齐次系统的局部拓扑结构，并给出利用系统右端多项式系数的判断准则。

2·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。