Geodesic
Korteweg--de Vries hierarchy as an~asymptotic limit of the~Boussinesq
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 294-304

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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.
Keywords: nonlinear equation, small parameter, potentiated Korteweg–de Vries equation, Lie–Bäcklund canonical operator, multiscale method, asymptotic representation
Mots-clés : soliton. 
@article{TMF_2008_154_2_a7,
     author = {S. A. Kordyukova},
     title = {Korteweg--de {Vries} hierarchy as an~asymptotic limit of {the~Boussinesq}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {294--304},
     publisher = {mathdoc},
     volume = {154},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a7/}
}
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S. A. Kordyukova. Korteweg--de Vries hierarchy as an~asymptotic limit of the~Boussinesq. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 294-304. http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a7/