Instability of standing waves for a system of nonlinear Schr\"odinger   equations in a degenerate case
  We study a system of nonlinear Schr\"odinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions are studied for both non-degenerate and degenerate cases. 
Shotaro Kawahara, Masahito Ohta
math.AP