THE KDV AND RLW SETS

It is shown that the well-known (1 + 1)-dimension equations of Kortewe g-de Vries (KdV), Boussinesq (BSQ) and regulated long waves (RLW) have a ''latent structure'', the latter connected with the KdV and RLW set s. The elements of these sets are solition-like equations of the KdV(t au, alpha) and RLW(tau, ) type, where tau greater than or equal to 1 i s the order of higher derivative with respect to t and the parameter a lpha > 0 defines the ''modification'' of the above input equations. Fo r example, KdV(1, 1) = KdV, KdV(1, 1/2)= mKdV,...,KdV(2, 1) = BSQ, KdV (2, 1/2)= mBSQ,...;RLW(1, 1) = RLW, RLW(1, 1/2) = mRLW, etc.