On a quasilinear Zakharov system describing laser-plasma interactions. (English) Zbl 1174.35528

Colin, M.; Colin, T.

Differ. Integral Equ. 17, No. 3-4, 297-330 (2004).

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

Keywords:

Euler-Maxwell system; laser-plasma interaction; hyperbolic-elliptic system