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. 
Luc Molinet (LAGA), Jean-Claude Saut (LM-Orsay), Nikolay Tzvetkov   (LPP)