Benjamin-Ono equation: Rogue waves, generalized breathers, soliton bending, fission, and fusion
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Benjamin-Ono equation: Rogue waves, generalized breathers, soliton bending, fission, and fusion Sudhir Singh1,a , K. Sakkaravarthi2,3,b , K. Murugesan1,c , R. Sakthivel4,d 1 Department of Mathematics, National Institute of Technology, Tiruchchirappalli, Tamil Nadu 620015,
India
2 Department of Physics, National Institute of Technology, Tiruchchirappalli, Tamil Nadu 620015, India 3 Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchchirappalli,
Tamil Nadu 620024, India
4 Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu 641046, India
Received: 2 April 2020 / Accepted: 25 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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 secondorder 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.
1 Introduction The study of water waves gains tremendous interest over more than two centuries; theoretical and experimental investigations are continuously increasing to understand the dynamics of these waves [1]. These wave equations are modeled using prototype ordinary/partial/delay/fractional differential equations [2,3]. The nonlinear dynamics of waves associated with such model equations explore several exciting phenomena including wave mixing/breaking and interaction of several localized structures like solitons, breathers, lump solutions, and rogue waves, which have several applications in fluid dynamics, plasma, Bose– Einstein condensate, fiber optics, and even in finance [3,4]. These wave models also studied in the sense of weak-type fractional stochastic equations, where the analysis of these models is more general [5]. One of the most agreeable localized structure is soliton. It can be viewed as a classical solution structures of the integrable models. It is also well known that the stabil-
a e-mail: [email protected] b e-mail: [email protected] (corresponding author) c e-mail: [email protected] d e-mail: [email protected] (corresponding author)
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ity or identity-preserving nature of these solution structures even after the collisions enables them to have phenomenal applications in diverse areas of s
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