Abstract:
For the model of surface waves, we perform an asymptotic analysis with
respect to a small parameter $\varepsilon$ 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
$t\approx\varepsilon^{-2}$, where the Korteweg–de Vries approximation becomes
inapplicable.
Citation:
S. A. Kordyukova, “Korteweg–de Vries hierarchy as an asymptotic limit of the Boussinesq
system”, TMF, 154:2 (2008), 294–304; Theoret. and Math. Phys., 154:2 (2008), 250–259