Solitary waves with the Madelung fluid description: A generalized derivative nonlinear Schrodinger equation

Within the framework of the Madelung fluid description, we will derive bright and dark (including gray- and black-soliton) envelope solutions for a generalized derivative nonlinear Schrodinger model i partial derivative Psi/partial derivative t = partial derivative(2)Psi/partial derivative x(2) + i a partial derivative/partial derivative x (vertical bar Psi vertical bar(2)Psi) + b vertical bar Psi vertical bar(2)Psi, by virtue of the corresponding solitary wave solutions for the stationary Gardner equations. Note that we only consider the motion with stationary-profile current velocity case and exclude the motion with constant current velocity case for a not equal 0; on the other hand, our results are derived under suitable assumptions for the current velocity associated with corresponding boundary conditions of the fluid density, and under corresponding parametric constraints. (C) 2015 Elsevier B.V. All rights reserved.