  In this work, we construct various interesting localized wave structures of
the Benjamin-Ono equation describing the dynamics of deep water waves.
Particularly, we extract the rogue waves and generalized breather solutions
with the aid of bilinear form and by applying two appropriate test functions.
Our analysis reveals the control mechanism of the rogue waves with arbitrary
parameters to obtain both bright and dark type first and second-order rogue
waves. Additionally, a generalization of the homoclinic breather method, also
known as the three-wave method, is used for extracting the generalized
breathers along with bright, dark, anti-dark, rational solitons. Interestingly,
we have observed the manipulation of breathers along with soliton interaction,
bending, fission, and fusion. Our results are discussed categorically with the
aid of clear graphical demonstrations.
