Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 731-759 |
| Number of pages | 29 |
| Journal | Communications in Mathematical Physics |
| Volume | 319 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 2013 |
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