Stability of Solitary Waves for a Generalized Derivative Nonlinear   Schr\"odinger Equation
  We consider a derivative nonlinear Schr\"odinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the nonlinearity and, in some instances, their velocity. We illustrate these results with numerical simulations. 
Xiao Liu, Gideon Simpson, Catherine Sulem
nlin.PS math.AP