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We obtain exact solitary wave solutions of a variant of the generalizedderivative nonlinear Schrodinger\equation in 1+1 dimensions with arbitraryvalues of the nonlinearity parameter $\kappa$ in a Scarf-II potential. Thisvariant of the usual derivative nonlinear Schrodinger equation has theproperties that for real external potentials, the dynamics is derivable from aLagrangian. The solitary wave and trapped solutions have the same form as thoseof the usual derivative nonlinear Schrodinger equation. We show that thesolitary wave solutions are orbitally stable for $\kappa \leq 1$ We find newexact nodeless solutions to the bound states in the external complex potentialwhich are related to the static solutions of the equation. We also use acollective coordinate approximation to analyze the stability of the trappedsolutions when the external potential is real.

journal of physics. a, mathematical and theoretical

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