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 quasilinear part and is the key of this paper. This shows that the Cauchy problem is locally well-posed.
"On a quasilinear Zakharov system describing laser-plasma interactions." Differential Integral Equations 17 (3-4) 297 - 330, 2004.