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math.AP2009★ 1 cited
Random data Cauchy problem for supercritical Schrödinger equations
Laurent Thomann
In this paper we consider the Schrödinger equation with power-like nonlinearity and confining potential or without potential. This equation is known to be well-posed with data in a…
math.AP2006★ 2 cited
The WKB method and geometric instability for non linear Schrodinger equations on surfaces
Laurent Thomann
In this paper we are interested in constructing WKB approximations for the non linear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approxim…
math.AP2006
Geometric and projective instability for the Gross-Pitaevski equation
Laurent Thomann
Using variational methods, we construct approximate solutions for the Gross-Pitaevski equation which concentrate on circles in . These solutions will help to show that the $L…