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

TL;DR

This paper derives exact solitary wave solutions for a generalized derivative nonlinear Schrödinger equation with a Scarf-II potential, analyzes their stability, and introduces new bound state solutions, advancing understanding of nonlinear wave dynamics in external potentials.

Contribution

It provides new exact solutions and stability analysis for a generalized derivative nonlinear Schrödinger equation in a Scarf-II potential, including novel nodeless bound states.

Findings

Solitary wave solutions are orbitally stable for  .

New exact nodeless bound state solutions are identified.

Stability of trapped solutions analyzed using collective coordinate approximation.

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 $\kappa \leq 1$ 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.