完全可积二元一阶微分方程的局部分支

摘要

应用 Legendre 奇点理论研究具有ℝ+-简单且稳定1-参数积分图的完全可积二元一阶非线性偏微分方程的局部分支分类问题，得到了该方程局部分支的一般分类结果，利用该结果可以掌握当参数变动时该类系统定性性态发生变化的情况。%Using Legendre singularity theory, we studied the local bifurcations of completely integrable holonomic systems of 2-variable first-order non-linearity partial differential equations whose corresponding one-parameter integral diagrams are ℝ+-simple and stable so as to obtain the classification of local bifurcations.Based on the result,the qualitative state of this system can be estimated when the parameters are changed.