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Physically relevant soliton solutions of the resonant nonlinear Schrodinger(RNLS) equation with nontrivial boundary conditions, recently proposed fordescription of uniaxial waves in a cold collisionless plasma, are considered inthe Hirota bilinear approach. By the Madelung representation, the model istransformed to the reaction-diffusion analog of the NLS equation for which thebilinear representation, soliton solutions and their mutual interactions arestudied.Comment: 15 pages, 1 figure, talk presented in Workshop `Nonlinear Physics IV:  Theory and Experiment`, 22-30 June 2006, Gallipoli, Ital

Solitons of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions: Hirota bilinear method