Various forms of M-shaped rational, periodic cross kink waves and breathers for Bose–Einstien condensate model.

In this manuscript, various types of breather, periodic cross-kink and rational solitons, M-shaped rational solutions with one and two kink and multi-waves will be discussed for Bose–Einstien condensate (BEC) model. We will compute the Kuznetsov–Ma breather, Akhmediev breather and generalized breather along with discussion on the interaction between them. At the end we will present the graphical description for our newly obtained solutions. [ABSTRACT FROM AUTHOR]