Matter-wave solutions of Bose–Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields

We construct, through a further extension of the tanh-function method, the matter-wave solutions of Bose--Einstein condensates (BECs) with a three-body interaction. The BECs are trapped in a potential comprising the linear magnetic and the time-dependent laser fields. The exact solutions obtained include soliton solutions, such as kink and antikink as well as bright, dark, multisolitonic modulated waves. We realize that the motion and the shape of the solitary wave can be manipulated by controlling the strengths of the fields.