A multi-D model for Raman amplification

In this paper, we continue the study of the Raman amplification in plasmas that we have initiated in \cite{colins1} and \cite{colins2}. We point out that the Raman instability gives rise to three components. The first one is colinear to the incident laser pulse and counter propagates. In 2-D, the two other ones make a non-zero angle with the initial pulse and propagates forward. Furthermore they are symmetric with respect to the direction of propagation of the incident pulse. We construct a nonlinear system taking into account all these components and perform some 2-D numerical simulations