Abstract
Atangana conformable Boussinesq-like equations (NLACBEs) plays an important role in shape-memory alloys, nonlinear string and coupled electrical circuits. In this paper, we study the different analytical solutions of various types of NLACBEs like multi-wave, homoclinic breather approach, rogue waves, M-shaped rational solutions, lump with one kink, lump interaction with kink and rogue wave, periodic-cross lump, lump with two kink, periodic cross-kink and periodic solutions. We compute the essential relationship between lump interaction with kink and rogue wave, periodic cross-kink and other types of exact solutions by studying the unknown nonlinear confirmable differential equations for the corresponding parameters. We show the graphical representation for our retrieve analytical solutions to observe the behavior of effective waves.
•The analytical and computational solutions are obtained.•The Atangana conformable Boussinesq-like equation.•Weakly dispersive prorogation of waves structures.