Аннотация:Everybody is accustomed that nonlinear effects amplify with increasing amplitude or intensity of a wave.However, we shall consider here so-called STRONG NONLINEARITY OF THE FIRST TYPE (according to a classification introduced earlier by the authors) where nonlinear effects do not disappear even for infinitesimal amplitudes. Among these are MODULAR (M) and QUADRATICALLY-CUBIC (QC) nonlinearities. We consider generalizations of Hopf, Burgers, Korteweg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko equations. New physical phenomena are observed in such wave systems. Important examples aregiven.