# American Institute of Mathematical Sciences

April  2016, 36(4): 2347-2364. doi: 10.3934/dcds.2016.36.2347

## On the blow-up of solutions to the periodic modified integrable Camassa--Holm equation

 1 Department of Mathematics, Nanjing Forestry University, Nanjing 210036, China 2 Department of Mathematics, Southwest University, Chongqing 400715, China

Received  March 2015 Revised  April 2015 Published  September 2015

We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the periodic modified Camassa-Holm equation with cubic nonlinearity. The blow-up conditions and the blow-up rate are formulated in terms of the initial momentum density and the average initial energy.
Citation: Min Zhu, Shuanghu Zhang. On the blow-up of solutions to the periodic modified integrable Camassa--Holm equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 2347-2364. doi: 10.3934/dcds.2016.36.2347
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##### References:
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