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