ORBITAL STABILITY OF SOLITARY WAVES FOR THE NONLINEAR DERIVATIVE SCHRODINGER-EQUATION

Consider herein are the stability of the solitary waves e(-i omega t)e (i psi(x-vt))a(x-vt) for the following nonlinear quintic derivative Sc hrodinger equation. u(t) = iu(xx) + i(c(3) \u\(2) + c(5) \u\(4)) u + [ (s(0) + s(2) \u\(2))u](x), u is an element of R. For the case s(2) not equal 0, the abstract results of Grillakis et al. [5, 6] do not apply directly. By constructing three appropriate invariants of motion and detailed spectral analysis, we obtain the stability of the solitary wa ves. (C) 1995 Academic Press, Inc.