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

Abstract

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 $\kappa \le 1$ 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.

arXiv comment26 pages, 4 figures

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Cited by in corpus (1)

• Nonlinear Schrödinger equations with amplitude-dependent Wadati potentials