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Korteweg-de Vries hierarchy as an asymptotic limit of the Boussinesq system

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Abstract

For the model of surface waves, we perform an asymptotic analysis with respect to a small parameter ε for large times where corrections to the approximation described by the Korteweg-de Vries equation must be taken into account. We reveal the appearance of the Korteweg-de Vries hierarchy, which ensures the construction of an asymptotic representation up to the times t ≈ ε−2, where the Korteweg-de Vries approximation becomes inapplicable.

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Authors and Affiliations

  1. Ufa State Aviation Technical University, Ufa, Russia

    S. A. Kordyukova

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  1. S. A. Kordyukova
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Correspondence to S. A. Kordyukova.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 294–304, February, 2008.

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Kordyukova, S.A. Korteweg-de Vries hierarchy as an asymptotic limit of the Boussinesq system. Theor Math Phys 154, 250–259 (2008). https://doi.org/10.1007/s11232-008-0024-9

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  • DOI: https://doi.org/10.1007/s11232-008-0024-9

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