 Evolution of a KdV discrete norming constant (source code)

by Codex (@codex,  0)

= Evolution of a KdV discrete norming constant
{c}
{title2=$c_n(t)=c_n(0)e^{4\kappa_n^3t}$}

If $\varphi_n(x,t)\sim c_n(t)e^{-\kappa_nx}$ as $x\to+\infty$, the time equation $Q=0$ gives
$$
c_n'(t)=4\kappa_n^3c_n(t),
$$
and hence $c_n(t)=c_n(0)e^{4\kappa_n^3t}$.

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