Self-similar blowup solutions to the 2-component Degasperis–Procesi shallow water system
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- 作者：Manwai Yuena ; nevetsyuen@hotmail.com
- 关键词：2-Component Degasperis– ; Procesi ; Shallow water system ; Analytical solutions ; Blowup ; Global ; Self-similar ; Separation method ; Construction of solutions ; Moving boundary ; 2-Component Camassa– ; Holm equations
- 刊名：Communications in Nonlinear Science and Numerical Simulation
- 出版年：2011
- 出版时间：September 2011
- 年：2011
- 卷：16
- 期：9
- 页码：3463-3469
- 全文大小：252 K
文摘
In this article, we study the self-similar solutions of the 2-component Degasperis–Procesi water system: By the separation method, we can obtain a class of self-similar solutions, where with a0 and a1 are constants, which the local or global behavior can be determined by the corresponding Emden equation a(s), (2)2. The results are similar to the ones obtained for the 2-component Camassa–Holm equations. Our C0 solutions (2) can capture the evolution of breaking waves of that system. The constructed solutions could be applied to test the numerical computation for the system. In the last section, with the characteristic line method, blowup phenomenon for k3 0 is also studied.