Bifurcation from semi-trivial standing waves and ground states for a   system of nonlinear Schr\"{o}dinger equations
  We consider a system of nonlinear Schr\"{o}dinger equations related to the Raman amplification in a plasma. We study the orbital stability and instability of standing waves bifurcating from the semi-trivial standing wave of the system. The stability and instability of the semi-trivial standing wave at the bifurcation point are also studied. Moreover, we determine the set of the ground states completely. 
Mathieu Colin and Masahito Ohta
math.AP