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Evolution of a KdV discrete norming constant ( $c_{n} (t) = c_{n} (0) e^{4 κ_{n}^{3} t}$ )

If

φ_{n} (x, t) \sim c_{n} (t) e^{- κ_{n} x}

as

x \to + \infty

, the time equation

Q = 0

gives

c_{n}^{'} (t) = 4 κ_{n}^{3} c_{n} (t),

and hence

c_{n} (t) = c_{n} (0) e^{4 κ_{n}^{3} t}

.

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