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A decay property of solutions to the \(k\)-generalized KdV equation. (English) Zbl 1261.35130

Summary: We use a Leibniz-rule-type inequality for fractional derivatives to prove conditions under which a solution \(u(x,t)\) of the \(k\)-generalized KdV equation is in the space \(L^2(|x|^{2s}dx)\) for \(s \in \mathbb R_+\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B40 Asymptotic behavior of solutions to PDEs
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