Geodesic
Solitons of the~resonant nonlinear Schr\"odinger equation with
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 133-146

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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.
Keywords: resonant nonlinear Schrödinger equation, quantum potential, cold plasma, magnetoacoustic wave, Hirota method.
Mots-clés : soliton 
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J.-H. Lee; O. K. Pashaev. Solitons of the~resonant nonlinear Schr\"odinger equation with. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 133-146. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a9/