= Local conserved-charge hierarchy of sine-Gordon theory
{title2=$\partial_\eta P_j=\partial_\xi Q_j$}
The Bäcklund expansion produces local differential-polynomial currents. In the coordinates $\xi=m(x+t)/2$, $\eta=m(x-t)/2$, their charges are $\int(P_j+Q_j)dx$ with vanishing boundary flux. Derivative improvements contribute no new charge. The first nontrivial higher current can be written $P=u_{\xi\xi}^2-u_\xi^4/4$, $Q=\cos u\,u_\xi^2$. Continuing, and exchanging light-cone directions, produces the infinite higher-spin hierarchy characterizing <classical integrability>.
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