4 papers
Non-existence of internal mode for small solitary waves of the 1D Zakharov system
Yvan Martel, Guillaume Rialland
We prove that the linearised operator around any sufficiently small solitary wave of the one-dimensional Zakharov system has no internal mode. This spectral result, along with its…
Continuum of finite point blowup rates for the critical generalized Korteweg-de Vries equation
Yvan Martel, Didier Pilod
For any , we prove the existence of an solution of the mass critical generalized Korteweg-de Vries equation on the time interval , for s…
Asymptotic analysis of small energy breathers for the nonlinear Klein-Gordon equation
MichaÅ Kowalczyk, Yvan Martel
For a class of nonlinear Klein-Gordon equations, we prove that in the small energy limit, any sequence of breathers decomposes into a finite sum of decoupled, periodically modulate…
A new proof of a Liouville theorem for the one dimensional Gross-Pitaevskii equation
MichaÅ Kowalczyk, Yvan Martel
The asymptotic stability of the black and dark solitons of the one-dimensional Gross-Pitaevskii equation was proved by Béthuel, Gravejat and Smets (Ann. Sci. Ãc. Norm. Supér. 48…