200 citations · 546 across the 22 of their papers we have counts for
7 papers · 2 filters
Transverse nonlinear instability for two-dimensional dispersive models
F. Rousset, N. Tzvetkov
We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solita…
On global Strichartz estimates for non trapping metrics
Jean-Marc Bouclet, Nikolay Tzvetkov
We prove global Strichartz estimates (with spectral cutoff on the low frequencies) for non trapping metric perturbations of the Schroedinger equation, posed on the Euclidean space.
Global well-posedness for the KP-I equation on the background of a non localized solution
Luc Molinet, Jean-Claude Saut, Nikolay Tzvetkov
We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not de…
Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation
N. Tzvetkov
We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures…
On finite energy solutions of the KP-I equation
Herbert Koch, Nikolay Tzvetkov
We prove that the flow map of the Kadomtsev-Petviashvili-I (KP-I) equation is not uniformly continuous on bounded sets of the natural energy space.
Remarks on the mass constraint for KP type equations
Luc Molinet, Jean-Claude Saut, Nikolay Tzvetkov
For a rather general class of equations of Kadomtsev-Petviashvili (KP) type, we prove that the zero-mass (in ) constraint is satisfied at any non zero time even if it is not sat…