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

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

Feb 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008tmp...154..250k&link_type=abstract

Theoretical and Mathematical Physics, Volume 154, Issue 2, pp.250-259

Mathematics

Mathematical Physics

Nonlinear Equation, Small Parameter, Potentiated Korteweg-De Vries Equation, Lie-B&Auml, Cklund Canonical Operator, Multiscale Method, Asymptotic Representation, Soliton

Scientific paper

For the model of surface waves, we perform an asymptotic analysis with respect to a small parameter ɛ 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 ≈ ɛ-2, where the Korteweg-de Vries approximation becomes inapplicable.

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