  Physically relevant soliton solutions of the resonant nonlinear Schrodinger
(RNLS) equation with nontrivial boundary conditions, recently proposed for
description of uniaxial waves in a cold collisionless plasma, are considered in
the Hirota bilinear approach. By the Madelung representation, the model is
transformed to the reaction-diffusion analog of the NLS equation for which the
bilinear representation, soliton solutions and their mutual interactions are
studied.
