Abstract
We have exploited the theory of Madelung fluid description in order to retrieve the correspondence between the envelope soliton like solutions of a generalized derivative resonant nonlinear Schrödinger equation (GDRNLSE) and the soliton like solutions of a stationary generalized Gardner equation. The motion under consideration was with stationary profile current velocity only and under suitable assumptions on current velocity in context of corresponding boundary conditions of fluid velocity and parametric constraints, the results were obtained. We mainly derived bright and dark (which involves grey and black) envelope soliton like solutions along with periodic wave envelope solutions having a phase depending on both space and time of the generalized derivative resonant nonlinear Schrödinger equation recovered from the corresponding solitary waves and periodic wave solutions of the stationary generalized Gardner equation.
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