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

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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 a weak convergence to a nonlinear Schrödinger equation.

    Mathematics Subject Classification: Primary: 35Q35; Secondary: 35Q55.


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