Exact solutions of a generalized variant of the derivative nonlinear Schrodinger equation in a Scarff II external potential and their stability properties

We obtain exact solitary wave solutions of a variant of the generalized derivative nonlinear Schrodinger equation in 1+1 dimensions with arbitrary values of the nonlinearity parameter kappa in a Scarf-II potential. This variant of the usual derivative nonlinear Schrodinger equation has the properties that for real external potentials, the dynamics is derivable from a Lagrangian. The solitary wave and trapped solutions have the same form as those of the usual derivative nonlinear Schrodinger equation. We show that the solitary wave solutions are orbitally stable for kappa <= 1. We find new exact nodeless solutions to the bound states in the external complex potential which are related to the static solutions of the equation. We also use a collective coordinate approximation to analyze the stability of the trapped solutions when the external potential is real.