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KdV suggests a connection between waves in shallow water and the potential in the Schrödinger equation. What is the intuitive explanation?
The KdV equation
$$v_t+\frac{1}{4}v_{xxx}-\frac{3}{2}vv_x=0$$
was originally invented to model waves in shallow water.
However, it is well known that it also has applications in quantum mechanics. ...
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