### A decay property of solutions to the k-generalized KdV equation

Joules Nahas

#### Abstract

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 $s \in \mathbb R_{+}$.

#### Article information

Source
Adv. Differential Equations Volume 17, Number 9/10 (2012), 833-858.

Dates
First available in Project Euclid: 17 December 2012