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I know that KdV is a balance of the nonlinearity and the dispersive effect and hence the wave profile propagates permenantly without disperse.

However, why one always mention that it is the balance of WEAKLY nonlinear and WEAKLY dispersive?

Can't it be a balance of STRONGLY nonlinear and STRONLY dispersive?

Will the KdV equation still exist if the shallow water parameter and the nonlinear parameter does not tend to zero but just with the same order of magnitude? Nnamely O(d^2) = O(epsilon), yet, not tends to zero.

Can someone kindly help?