Solitons of the Resonant Nonlinear Schrodinger Equation with Nontrivial   Boundary Conditions and Hirota Bilinear Method
  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. 
Jyh-Hao Lee and Oktay K. Pashaev