https://doi.org/10.1140/epjp/s13360-020-00808-8
Regular Article
Benjamin-Ono equation: Rogue waves, generalized breathers, soliton bending, fission, and fusion
1
Department of Mathematics, National Institute of Technology, 620015, Tiruchchirappalli, Tamil Nadu, India
2
Department of Physics, National Institute of Technology, 620015, Tiruchchirappalli, Tamil Nadu, India
3
Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, 620024, Tiruchchirappalli, Tamil Nadu, India
4
Department of Applied Mathematics, Bharathiar University, 641046, Coimbatore, Tamil Nadu, India
b
ksakkaravarthi@gmail.com
d
krsakthivel@yahoo.com
Received:
2
April
2020
Accepted:
25
September
2020
Published online:
13
October
2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
