39 citations · 72 across the 7 of their papers we have counts for
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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…
Amplitude equations for weakly nonlinear surface waves in variational problems
Sylvie Benzoni-Gavage, Jean-François Coulombel
Among hyperbolic Initial Boundary Value Problems (IBVP), those coming from a variational principle 'generically' admit linear surface waves, as was shown by Serre [J. Funct. Anal.…
The amplitude equation for weakly nonlinear reversible phase boundaries
Jean-François Coulombel, Sylvie Benzoni-Gavage
This technical note is a complement to an earlier paper [Benzoni-Gavage \& Rosini, Comput. Math. Appl. 2009], which aims at a deeper understanding of a basic model for propagating…
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…
Stability of periodic waves in Hamiltonian PDEs
Sylvie Benzoni-Gavage, Pascal Noble, Luis Miguel Rodrigues
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich fami…
Slow modulations of periodic waves in Hamiltonian PDEs, with application to capillary fluids
Sylvie Benzoni-Gavage, Pascal Noble, Luis Miguel Rodrigues
Since its elaboration by Whitham, almost fifty years ago, modulation theory has been known to be closely related to the stability of periodic traveling waves. However, it is only r…
On a phase field model for solid-liquid phase transitions
Sylvie Benzoni-Gavage, Laurent Chupin, Didier Jamet +1
A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms.…