Abstract:
In the first section of this article a new method for computing the densities of integrals of motion for the KdV equation is given. In the second section the variation with respect to $q$ of the functional $\int_0^\pi W(x,t,x;q)\,dx$ ($t$ is fixed) is computed, where $W(x,t,x;q)$ is the Riemann function of the problem
\begin{gather*}
\frac{\partial^2u}{\partial x^2}-q(x)u=\frac{\partial^2u}{\partial t^2}\quad(-\infty<x<\infty),
\\
u|_{t=0}f=(x),\quad\frac{\partial u}{\partial t}\Bigr|_{t=0}=0.
\end{gather*}
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