中文摘要：

本文利用动力系统的定性分析理论研究了K（3，2）方程ut＋（u3）x＋（U2）xxx=0的分支问题，并利用Maple软件进行数值模拟得到行波解系统相应的相图，然后通过积分计算得到周期尖波和孤立波的精确解表达式．本文补充了方程K（3，2）的研究结果．

英文摘要：

Bifurcation of K（3,2） equation ut ＋ （u3 ）x ＋ （u2 ）xxx = 0 with osmosis dispersion is discussed and investigated by means of the qualitative analysis methods of dynamical system. Illustrative phase portraits corresponding to traveling wave system are presented after numerical simulation by Maple pro- grams. Expressions of the periodic cusp wave and implicit expressions of soliton are explicitly given. It enriches the known results of K（3,2）.