Local well-posedness for the Zakharov system on the background of a line soliton

Abstract

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 Schrödinger equation.

arXiv comment24 pages, revised version