Orbital stability of the Degasperis-Procesi equation

Orbital stability of the Degasperis-Procesi equation

At the invitation of Center for Mathematical Sciences, Professor Ji Li from Huazhong University of Science and Technologygave an online talk titled “Orbital stability of the Degasperis-Procesi equation” on Mar 24th, 2021. Teachers and students in School of Mathematics and Physics in related research fields attended this academic colloquium.

The Degasperis-Procesi equation is an approximating model of shallow-water wave propagating mainly in one direction to the Euler equation. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations with the same asymptotic accuracy, and is completely integrable with the bi-Hamiltonian structure. In the present study, Prof. Li establishedthe existence and stability of localized smooth solitons to the DP equation on the real line. The spectral stability relies essentially on refined spectral analysis of the linear operator corresponding to the second-order variational derivative of the local Hamiltonian. The orbital stability relies on  some tricky L^p controll.