A multi-D model for Raman amplification
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 1, p. 1-22

In this paper, we continue the study of the Raman amplification in plasmas that we initiated in [Colin and Colin, Diff. Int. Eqs. 17 (2004) 297-330; Colin and Colin, J. Comput. Appl. Math. 193 (2006) 535-562]. We point out that the Raman instability gives rise to three components. The first one is collinear 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 propagate forward. Furthermore they are symmetric with respect to the direction of propagation of the incident pulse. We construct a non-linear system taking into account all these components and perform some 2-D numerical simulations.

DOI : https://doi.org/10.1051/m2an/2010037
Classification:  35Q55,  35Q60,  78A60,  74S20
Keywords: Raman amplification, Zakharov system, weakly nonlinear theory
@article{M2AN_2011__45_1_1_0,
     author = {Colin, Mathieu and Colin, Thierry},
     title = {A multi-D model for Raman amplification},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {1},
     year = {2011},
     pages = {1-22},
     doi = {10.1051/m2an/2010037},
     zbl = {06183193},
     mrnumber = {2781129},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_1_1_0}
}
Colin, Mathieu; Colin, Thierry. A multi-D model for Raman amplification. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 1, pp. 1-22. doi : 10.1051/m2an/2010037. http://www.numdam.org/item/M2AN_2011__45_1_1_0/

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