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Blow-up phenomenon for the integrable Degasperis-Procesi equation. (English) Zbl 1134.37361
Summary: We investigate a new integrable equation derived recently by Degasperis and Procesi. Analogous to the Camassa-Holm equation, this new equation possesses the blow-up phenomenon. Under the special structure of this equation, we establish sufficient conditions on the initial data to guarantee the formulation of a singularity in the sense that the derivative of the solution blows up in finite time. Moreover, a global existence result is found.

37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35Q58Other completely integrable PDE (MSC2000)
Full Text: DOI
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