Dispersion via modulation in shallow water

What is it about?

A new theory for the emergence of dispersion in shallow water hydrodynamics is presented. Starting with the key properties of uniform flow in open-channel hydraulics, it is shown that criticality is the key mechanism for generating the KdV and KP equations. An implication of the theory is that the coefficient of nonlinearity in the KdV and KP equatoins are obtained by an elementary calculation.

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Why is it important?

Gives a new mechanism for the emergence of the KdV and KP equations in shallow water hydrodynamics, which is closer to the physics and is at the same time simpler theoretically.