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Multiple Lump and Rogue Wave Solutions of a Modified Benjamin-Ono Equation

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Nonlinear and Modern Mathematical Physics (NMMP 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 459))

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Abstract

In this chapter, a (2+1)-dimensional modified Benjamin-Ono (MBO) equation is introduced. Multiple lump (M-lump) and rogue wave solutions are obtained for the equation with the aid of the Hirota bilinear method. The equation is first studied in two parts: an integrable and a nonintegrable part. The nonintegrable part is found to possess 1-lump and line rogue wave solutions whereas the integrable part has only 1-lump solutions. Furthermore, the MBO equation is found to posses both multiple lump and rogue wave solutions. By fixing parameter values, the dynamics of the solutions are studied with 3D and density plots.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Florida A & M University, Tallahassee, FL, 32307, USA

    Solomon Manukure

  2. School of Data Science, **anda College of Economics & Humanities Shanghai International Studies University, Shanghai, 200083, China

    Yuan Zhou

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  1. Solomon Manukure
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  2. Yuan Zhou
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Correspondence to Yuan Zhou .

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Editors and Affiliations

  1. Department of Mathematics, Florida A&M University, Tallahassee, FL, USA

    Solomon Manukure

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, USA

    Wen-**u Ma

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Manukure, S., Zhou, Y. (2024). Multiple Lump and Rogue Wave Solutions of a Modified Benjamin-Ono Equation. In: Manukure, S., Ma, WX. (eds) Nonlinear and Modern Mathematical Physics. NMMP 2022. Springer Proceedings in Mathematics & Statistics, vol 459. Springer, Cham. https://doi.org/10.1007/978-3-031-59539-4_12

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