111 citations · 563 across the 42 of their papers we have counts for
47 papers
Classification of multi-solitons in one sense of time for the 5D energy-critical wave equation
Yvan Martel, Frank Merle
We classify the multi-solitons, in the positive sense of time, of the focusing energy-critical wave equation in space dimension , more precisely the solutions of the eq…
Existence of multi-solitons with any parameters for the 5D energy critical wave equation
Yvan Martel, Frank Merle
For the focusing, energy critical wave equation in dimension 5, we construct multi-solitons with any number of solitons, any choice of signs, speeds, scaling parameters and transla…
Non-flat conformal blow-up profiles for the 1D critical nonlinear Schrödinger equation
Yvan Martel, Ivan Naumkin
For the critical one-dimensional nonlinear Schrödinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a non-f…
Kink dynamics under odd perturbations for (1+1)-scalar field models with one internal mode
Michał Kowalczyk, Yvan Martel
We consider odd symmetric (1+1)-scalar field models with one internal mode. Under natural and robust assumptions, including the Fermi golden rule, we prove the asymptotic stability…
Asymptotic stability of solitary waves for the 1D cubic-quintic Schrödinger equation with no internal mode
Yvan Martel
For the Schrödinger equation with a cubic-quintic, focusing-defocusing nonlinearity in one space dimension, we prove the asymptotic stability of solitary waves for a large range of…
Finite point blowup for the critical generalized Korteweg-de Vries equation
Yvan Martel, Didier Pilod
In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determi…