We study the solutions of a quasilinear Schrödinger equation which has been derived in many areas of physical modeling. Using the Morawetz Radial Identity, we show that the local energy of a solution is integrable in time and the local $L^2$ norm of the solution approaches zero as time approaches the infinity.
"Local Time Decay for a Quasilinear Schrodinger Equation." Methods Appl. Anal. 16 (3) 313 - 320, September 2009.