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On a degenerate Zakharov system. (English) Zbl 1070.35087
Summary: We establish a local well-posedness result for an initial value problem associated to a Zakharov system arising in the study of laser-plasma interactions. We call this system degenerate due to the lack of dispersion presented in one of the spatial variables. One of the key tools to obtain our results is the presence of appropriate global versions of the so called “local smoothing effects” inherent to the dispersive character of the model.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
78A60 Lasers, masers, optical bistability, nonlinear optics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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