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The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system where . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L 2 -subcritical σ (that is σ ≤ 2/3) and the H 1 -subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the norm.

A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence