Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 319, Issue 3, Pages 731-759Publisher
SPRINGER
DOI: 10.1007/s00220-012-1566-0
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Funding
- NSF of China [11001111, 11171241]
- Jiangsu University [10JDG141, 10JDG157]
- NSF [DMS-0906099, DMS-1207840, DMS-1108894]
- NHARP [003599-0001-2009]
- NSF-China [11271192]
- NSF-China for Distinguished Young Scholars [10925104]
- Ph.D. Programs Foundation of Ministry of Education of China [20106101110008]
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In this paper, we investigate the formation of singularities and the existence of peaked traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The equation is known to be integrable, and is shown to admit a single peaked soliton and multi-peakon solutions, of a different character than those of the Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and a new wave-breaking mechanism for solutions with certain initial profiles is described in detail.
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