Bifurcations of travelling wave solutions in a new integrable equation with peakon and compactons
Bifurcations of travelling wave solutions in a new integrable equation with peakon and compactons
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DOI：
10.1016/j.chaos.2005.04.020
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发表时间：
2006
影响因子：
7.8
通讯作者：
Jianwei Shen;W. Xu;Wei Li
中科院分区：
文献类型：
--
作者：
Jianwei Shen;W. Xu;Wei Li
Degasperis和Procesi应用渐近可积方法，得到Degasperis-Procesi方程。他们证明了它有peakon解，该解在波峰处具有不连续的一阶导数，但他们没有解释peakon解出现的原因。本文研究了广义Degasperis-Procesi方程ut−utxx+(b+1)uux=buxuxx+uuxxx的这些非光滑解，揭示了非光滑行波产生的原因，并研究了全局动力学行为，得到了peakon、compacton和其他行波解产生的参数条件。在一定参数条件下，该方程有无穷多个compacton解。最后，我们给出了peakon和compacton解的一些显式表达。
Degasperis and Procesi applied the method of asymptotic integrability and obtain Degasperis–Procesi equation. They showed that it has peakon solutions, which has a discontinuous first derivative at the wave peak, but they did not explain the reason that the peakon solution arises. In this paper, we study these non-smooth solutions of the generalized Degasperis–Procesi equation ut−utxx+(b+1)uux=buxuxx+uuxxx, show the reason that the non-smooth travelling wave arise and investigate global dynamical behavior and obtain the parameter condition under which peakon, compacton and another travelling wave solutions engender. Under some parameter condition, this equation has infinitely many compacton solutions. Finally, we give some explicit expression of peakon and compacton solutions.