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海洋环流与波动系列学术报告(20150517)

时间:2015-05-21  来源: 文本大小:【 |  | 】  【打印

报告题目:A generalized Camassa-Holm equation and its peakon solutions

报告人:Zhijun Qiao, Ddpt. of  Mathematics University of Texas-Pan American

报告时间:2015.5.17

报告内容:

 

In this work, we study an integrable system with both quadratic and cubic nonlinearity. This model is kind of a cubic generalization of the Camassa-Holm (CH) equation. The equation is shown integrable with its Lax pair, bi-Hamiltonian structure, and infinitely many conservation laws. In the case of b = 0, the peaked soliton (peakon) and multi-peakon solutions are presented. In particular, the two-peakon dynamical system is explicitly presented and their collisions are investigated in details. In some special case, the weak kink and kink-peakon interactional solutions are found. Significant difference from the CH equation is analyzed through a comparison. In the paper, we also study all possible smooth one-soliton solutions for the system.

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