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 modified integrable Camassa-Holm equation with cubic nonlinearity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.
Bibliographical noteFunding Information:
The work of Liu is partially supported by the NSF grant DMS-1207840 and the NSF-China grant 11271192. The work of Olver is partially supported by NSF grant DMS-1108894. The work of Qu is supported in part by the NSF-China for Distinguished Young Scholars grant 10925104. The work of Zhang is partially supported by the NSF of China under the grant 11101337, Doctoral Foundation of Ministry of Education of China grant 20110182120013, Fundamental Research Funds for the Central Universities grant XDJK2011C046, and China Scholarship Council.
- Blow up
- Integrable equation
- Modified Camassa-Holm equation