Local well-posedness for the Zakharov system on the background of a line soliton
classification
🧮 math.AP
keywords
systemzakharovlineprovebackgroundcauchyconvergencedata
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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.
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