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Benjamin-Ono equation: Rogue waves, generalized breathers, soliton bending, fission, and fusion

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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 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.

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Acknowledgements

SS is grateful to Ministry of Human Resource Development (MHRD), Government of India, and National Institute of Technology, Tiruchirappalli, India, for financial support through institute fellowship. The work of KS was supported by Department of Science and Technology - Science and Engineering Research Board (DST-SERB), Government of India, National Post-Doctoral Fellowship (File No. PDF/2016/000547). Authors thank the anonymous reviewer for providing fruitful comments for the betterment of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Tiruchchirappalli, Tamil Nadu, 620015, India

    Sudhir Singh & K. Murugesan

  2. Department of Physics, National Institute of Technology, Tiruchchirappalli, Tamil Nadu, 620015, India

    K. Sakkaravarthi

  3. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchchirappalli, Tamil Nadu, 620024, India

    K. Sakkaravarthi

  4. Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, 641046, India

    R. Sakthivel

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  1. Sudhir Singh
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  2. K. Sakkaravarthi
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  3. K. Murugesan
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  4. R. Sakthivel
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Contributions

SS helped in conceptualization; methodology; writing—original draft, review, and editing. KS contributed to formal analysis; investigation; visualization; writing—original draft, review, and editing. KM helped in funding acquisition; resources; supervision; project administration. RS contributed to resources; supervision; project administration.

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Correspondence to K. Sakkaravarthi or R. Sakthivel.

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Singh, S., Sakkaravarthi, K., Murugesan, K. et al. Benjamin-Ono equation: Rogue waves, generalized breathers, soliton bending, fission, and fusion. Eur. Phys. J. Plus 135, 823 (2020). https://doi.org/10.1140/epjp/s13360-020-00808-8

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