# American Institute of Mathematical Sciences

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December  2016, 9(6): 2149-2165. doi: 10.3934/dcdss.2016089

## Wave breaking and persistent decay of solution to a shallow water wave equation

 1 Business School of Central South University, Changsha 410012, China 2 Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

Received  June 2015 Revised  September 2016 Published  November 2016

As we all know, wave breaking of the water wave is important and interesting to physicist and mathematician. In the article, we devote to the study of blow-up phenomena, the decay of solution and traveling wave solution to a shallow water wave equation. First, based on the blow-up scenario, some new blow-up phenomena is derived. By virtue of a weighted function, the persistent decay of solution is established. Finally, we explore the analytic solutions and traveling wave solutions.
Citation: Xue Yang, Xinglong Wu. Wave breaking and persistent decay of solution to a shallow water wave equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2149-2165. doi: 10.3934/dcdss.2016089
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