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中文摘要：
本文利用动力系统分岔理论和广义函数理论，并结合相图分析的方法对广义Degasperis-Proces方程的非解析波解进行了研究，给出了不同非解析波存在的分岔条件，并给出了这些非解析行波解的精确参数表达式，此外本文对不同非解析行波解进行了分类，证明了Peakon解和Vallyon解是广义解而非弱解，而Compacton解是弱解。本文提出的方法为非线性波方程的非解析行波解的研究提供了一条可行的思路，给出的结论丰富了非解析行波解的研究结果。
英文摘要：
By using the theory of generalized function and bifurcation theory, we studied the non- analytic wave solutions of the generalized Degasperis-Procesi equation, and obtained the bifurcations of different non-analytic wave solutions which had arisen and the explicit expression of these non-analytic wave solutions. In the meantime, we classified the different non-analytic wave solutions and proved that Peakon and Valleyon are generalized solutions and the Compacton is weak solution.
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