Local well-posedness for the Zakharov system on the background of a line   soliton
  We prove that the Cauchy problem for the two-dimensional Zakharov system is locally well-posed for initial data which are localized perturbations of a line solitary wave. Furthermore, for this Zakharov system, we prove weak convergence to a nonlinear Schr\"odinger equation. 
Hung Luong
math.AP