596 citations · 1.2k across the 49 of their papers we have counts for
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Near soliton dynamics and singularity formation for critical problems
Yvan Martel, Frank Merle, Pierre Raphael +1
This survey reviews the state of the art concerning the singularity formation for two canonical dispersive problems: the mass critical non linear Schrödinger equation and the mass…
On the nonexistence of pure multi-solitons for the quartic gKdV equation
Yvan Martel, Frank Merle
We consider the quartic (nonintegrable) (gKdV) equation. Let u(t) be an outgoing 2-soliton of the equation, i.e. a solution behaving exactly as the sum of two solitons (of speeds c…
Type II blow up for the energy supercritical NLS
Frank Merle, Pierre Raphael, Igor Rodnianski
We consider the energy super critical nonlinear Schrödinger equation $$i\pa_tu+Δu+u|u|^{p-1}=0$$ in large dimensions with spherically symmetric data. For all la…
Solutions of the focusing nonradial critical wave equation with the compactness property
Thomas Duyckaerts, Carlos E. Kenig, Frank Merle
Consider the focusing energy-critical wave equation in space dimension 3, 4 or 5. In a previous paper, we proved that any solution which is bounded in the energy space converges, a…