Envelope bright- and dark-soliton solutions for the Gerdjikov Ivanov model

Abstract

Within the context of the Madelung fluid description, investigation has been carried out on the connection between the envelope soliton-like solutions of a wide family of nonlinear Schrödinger equations and the soliton-like solutions of a wide family of Korteweg-de Vries or Korteweg-de Vries-type equations. Under suitable hypothesis for the current velocity, the Gerdjikov-Ivanov envelope solitons are derived and discussed in this paper. For a motion with the stationary profile current velocity, the fluid density satisfies a generalized stationary Gardner equation, which possesses bright- and dark-type (including gray and black) solitary waves due to associated parametric constraints, and finally envelope solitons are found correspondingly for the Gerdjikov-Ivanov model. Moreover, this approach may be useful for studying other nonlinear Schrödinger-type equations.