3 papers
math.AP2016
A Kam Theorem for Space-Multidimensional Hamiltonian PDE
L Hakan Eliasson, Benoit Grebert, Sergei Kuksin
We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: the in…
math.DS2014
KAM-tori near an analytic elliptic fixed point
H. Eliasson, B. Fayad, R. Krikorian
We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector $…
math.AP2007
KAM for the Non-Linear Schrödinger Equation
L. H. Eliasson, S. B. Kuksin
We consider the -dimensional nonlinear Schrödinger equation under periodic boundary conditions: $-i\dot u=-Δu+V(x)*u+\ep \frac{\p F}{\p \bar u}(x,u,\bar u), \quad u=u(t,x), x\in…