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Complex singularities in KdV solutions

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Abstract

In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.

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Acknowledgments

The work of F.G., G.P. and V.S. was partially supported by an INdAM-GNFM 2015 Progetto Giovani grant.

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Authors and Affiliations

  1. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Università degli Studi di Palermo, Palermo, Italy

    F. Gargano

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Palermo, Italy

    G. Ponetti, M. Sammartino & V. Sciacca

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  1. F. Gargano
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  2. G. Ponetti
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  3. M. Sammartino
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  4. V. Sciacca
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Correspondence to V. Sciacca.

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Gargano, F., Ponetti, G., Sammartino, M. et al. Complex singularities in KdV solutions. Ricerche mat 65, 479–490 (2016). https://doi.org/10.1007/s11587-016-0269-9

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