Soliton Solutions and their (In)stability for the Focusing   Davey-Stewartson II Equation
  We give a rigorous mathematical analysis of the one-soliton solution of the focusing Davey-Stewartson II equation and a proof of its instability under perturbation. Building on the fundamental perturbation analysis of Gadyl'shin and Kiselev, we verify their Assumption 1 and use Fredholm determinants to globalize their perturbation analysis. 
Peter A. Perry
math.AP math-ph math.MP