一类三阶色散方程的非解析波解的讨论

Discussion of the Peakon and compacton solutions for a class of dispersion equation of third order

利用分岔理论对一类三阶色散方程的非解析波解进行了研究,得出不同的非解析波解存在的条件,并得到Peakon解是广义解而非弱解的结论.

The non-analytical solution for a class of dispersion equation of third order is analyzed by using bifurcation theory and the method of phase portraits analysis. As a result, the analytic expression of Peakon solution is obtained. And the condition under which Peakon appears is also given. In the meantime, the conclusion that Peakon solution is the generalized solution but not a weak solution is proved.