Global well-posedness for the KP-II equation on the background of a non localized solution

Motivated by transverse stability issues, we address the time evolution under the KP-II flow of perturbations of a solution which does not decay in all directions, for instance the KdV-line soliton. We study two different types of perturbations : perturbations that are square integrable in \R\times \T and perturbations that are square integrable in $\R^2$. In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data

Madelung, Gross-Pitaevskii and Korteweg

This paper surveys various aspects of the hydrodynamic formulation of the nonlinear Schrodinger equation obtained via the Madelung transform in connexion to models of quantum hydrodynamics and to compressible fluids of the Korteweg type.Comment: 32 page

Remarks on the mass constraint for KP type equations

For a rather general class of equations of Kadomtsev-Petviashvili (KP) type, we prove that the zero-mass (in $x$) constraint is satisfied at any non zero time even if it is not satisfied at initial time zero. Our results are based on a precise analysis of the fundamental solution of the linear part and its anti $x$-derivative