×

zbMATH — the first resource for mathematics

On a quasilinear Zakharov system describing laser-plasma interactions. (English) Zbl 1174.35528
Summary: In this paper, starting from the bi-fluid Euler-Maxwell system, we derive a complete set of Zakharov-type equations describing laser-plasma interactions. This system involves a quasilinear part which is not hyperbolic and exhibits some elliptic zones. This difficulty is overcome by making a change of unknowns that are strongly related to the dispersive part. This change of variable is a symmetrization of the quasi-linear part and is the key of this paper. This shows that the Cauchy problem is locally well-posed.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q60 PDEs in connection with optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
PDF BibTeX XML Cite