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Changzheng Qu : Blow up solutions and stability of peakons to integrable equations with nonlinear dispersion

In this talk, we study blow-up mechanism of solutions to an integrable equation with cubic nonlinearities and nonlinear dispersion. We will show that singularities of the solutions can occur only in the form of wave-breaking. Some wave-breaking conditons on the initial data are provided. In addition, this equation is known to admit single and multi-peaked solitons, of a different character than those of the Camassa-Holm equation. We will prove that the shapes of these waves are stable under small perturbations in the energy space.

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