# American Institute of Mathematical Sciences

November  2018, 17(6): 2657-2682. doi: 10.3934/cpaa.2018126

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

 Fak. Mathematik, University of Vienna, Oskar MorgensternPlatz 1, A-1090 Wien, Austria

Received  March 2018 Revised  March 2018 Published  June 2018

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 a weak convergence to a nonlinear Schrödinger equation.

Citation: Hung Luong. Local well-posedness for the Zakharov system on the background of a line soliton. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2657-2682. doi: 10.3934/cpaa.2018126
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