Envelope bright– and dark–soliton solutions for the Gerdjikov Ivanov model
Yu, J. U. N.
Khalique, Chaudry Masood
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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.