18 citations · 32 across the 3 of their papers we have counts for
4 papers · 1 filter
Modulated equations of Hamiltonian PDEs and dispersive shocks
Sylvie Benzoni-Gavage, Colin Mietka, L. Miguel Rodrigues
Motivated by the ongoing study of dispersive shock waves in non integrable systems, we propose and analyze a set of wave parameters for periodic waves of a large class of Hamiltoni…
Stability of periodic waves in Hamiltonian PDEs of either long wavelength or small amplitude
Sylvie Benzoni-Gavage, Colin Mietka, Luis M. Rodrigues
Stability criteria have been derived and investigated in the last decades for many kinds of periodic traveling wave solutions to Hamiltonian PDEs. They turned out to depend in a cr…
On the well-posedness of a quasi-linear Korteweg-de Vries equation
Colin Mietka
The Korteweg-de Vries equation (KdV) and various generalized, most often semi- linear versions have been studied for about 50 years. Here, the focus is made on a quasi-linear gener…
Co-periodic stability of periodic waves in some Hamiltonian PDEs
Sylvie Benzoni-Gavage, Colin Mietka, L. Miguel Rodrigues
The stability of periodic traveling wave solutions to dispersive PDEs with respect to `arbitrary' perturbations is still widely open. The focus is put here on stability with respec…