Abstract
The Cauchy problem for the Korteweg–de Vries equation is considered with initial profile integrable against $(1 + | x |)dx$ on $\mathbb{R}$ and against $(1 + | x |)^N dx$ on $\mathbb{R}^ + $. Classical solutions are constructed for $N \geqq {{11} / 4}$. Under mild additional hypotheses the solution evolves in $L^2 (\mathbb{R})$.