Solitary Waves in a Madelung Fluid Description of Derivative NLS Equations

Recently using a Madelung fluid description a connection between envelope-like solutions of
NLS-type equations and soliton-like solutions of KdV-type equations was found and investigated
by R. Fedele et al. (2002). A similar discussion is given for the class of derivative
NLS-type equations. For a motion with stationary profile current velocity the fluid density
satisfies generalized stationary Gardner equation, and solitary wave solutions are found. For
the completely integrable cases these are compared with existing solutions in literature.