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.


37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35Q58 Other completely integrable PDE (MSC2000)
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