Non-Analyticity in Time of Solutions to the KdV Equation | Zendy

Grzegorz Łysik | Zendy

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Non-Analyticity in Time of Solutions to the KdV Equation

Author(s) -

Grzegorz Łysik

Publication year - 2004

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1188

Subject(s) - korteweg–de vries equation , mathematics , mathematical physics , mathematical analysis , physics , nonlinear system , quantum mechanics

It is proved that the formal power series solutions to the initial value problem @tu = @ 3 xu +@x(u 2 ), u(0;x) = '(x), where ' is analytic belong to the Gevrey class G 2 in time. However, if '(x) = 1=(1 +x 2 ), the solution does not belong to the Gevrey class G s in time for 0 s < 2. The proof is based on the estimation of a double sum of products of binomial coecients. 1. Introduction. We consider the characteristic Cauchy problem for the Korteweg- de Vries equation (1) @tu = @ 3 xu +@x(u 2 ); u(0;x) = '(x):

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