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Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1) pp 349–371Cite as

On the IVP for the k-Generalized Benjamin–Ono Equation

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Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 4))

Abstract

We shall study special properties of solutions to the IVP associated to the k-generalized Benjamin–Ono equation. We shall compare them with those for the k-generalized Korteweg-de Vries equation and for the k-generalized dispersive Benjamin–Ono equation. Also we shall discuss some open questions appearing in this subject.

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Acknowledgements

The author would like to thank German Fonseca, Felipe Linares, and Jean-Claude Saut for fruitful conversations concerning with this work.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    Gustavo Ponce

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  1. Gustavo Ponce
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Correspondence to Gustavo Ponce .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico, USA

    María Cristina Pereyra

  2. Department of Mathematics, Venezuelan Institute for Scientific Research, Caracas, Venezuela

    Stefania Marcantognini

  3. Department of Mathematical Sciences, Georgia Southern University, Statesboro, Georgia, USA

    Alexander M. Stokolos

  4. Department of Mathematics and Actu rial Science, Roosevelt University, Chicago, Illinois, USA

    Wilfredo Urbina

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Ponce, G. (2016). On the IVP for the k-Generalized Benjamin–Ono Equation. In: Pereyra, M., Marcantognini, S., Stokolos, A., Urbina, W. (eds) Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1). Association for Women in Mathematics Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-30961-3_16

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