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authorPrefetch2026-07-03 17:18:50 +0200
committerPrefetch2026-07-03 17:18:50 +0200
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treee9c9a3b2885c911bfeb101f74f93318264af328d /source/know/concept/korteweg-de-vries-equation/index.md
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@@ -152,7 +152,7 @@ rather than transform the coordinate system,
the velocity is incorporated into his ansatz for $$f$$;
in other words, he assumed that the entire liquid is moving at $$q_0$$.
For a wave going in the positive $$x$$-direction,
-the linearized problem then predicts a profile $$\eta(x \!-\! (\sqrt{g h} \!+\! q_0))$$,
+the linearized problem then predicts a profile $$\eta(x \!-\! (\sqrt{g h} \!+\! q_0) t)$$,
so de Vries chose $$q_0 = -\sqrt{g h}$$ to make it stationary.
Analogously, $$q_0 = \sqrt{g h}$$ for a backward-moving wave.
With this in mind, the ansatz is: