Abstract:
We use the Hirota bilinear approach to consider physically relevant soliton
solutions of the resonant nonlinear Schrödinger equation with nontrivial
boundary conditions, recently proposed for describing uniaxial waves in
a cold collisionless plasma. By the Madelung representation, the model
transforms into the reaction–diffusion analogue of the nonlinear
Schrödinger equation, for which we study the bilinear representation,
the soliton solutions, and their mutual interactions.