Phase Engineering and Solitons of Bose-Einstein Condensates with Two- and Three-Body Interactions

We introduce a phase imprint into the macroscopic order parameter governing the dynamics of Bose-Einstein condensates with attractive two-body interactions described by a cubic Gross-Pitaevskii (GP) equation and then engineer the imprinted phase suitably to generate the modified GP equation. The modified GP equation describes the dynamics of condensates with both two-(attractive) and three-body (attractive and repulsive) interactions in an expulsive harmonic trap. Employing gauge transformation approach, we then construct bright solitons of the modified GP equation. We observe that the attractive three-body interactions introduce an additional nontrivial phase in the matter wave solitons arising due to attractive two-body interactions without changing their density while the repulsive three-body interactions enormously increase the density of the condensates without causing any change in the phase of the solitons originating from attractive two-body interactions.