Modified Scattering States for Subcritical Derivative Nonlinear Schrödinger Equations

Abstract

We consider the derivative nonlinear Schrodinger equationswhere the coefficient a(t) satisfies the condition Ja(t)J 5 C(l + ) t~) ' -~, 0 c S c 1 ,~ is a sufficiently small constant and Al, h6 E R, h2, A3, A4, h5 E C, h2 -A3 E R, A4 -A5 E R. We suppose that the initial data satisfy the exponential decay conditions. Then in the case A1 = 0, hz -A3 = 0 , A4 -h5 = 0, A6 = 0 we show that the usual scattering states exist, and in the other case we construct the modified scattering states.