Brand-new equations which can be regarded as modifications of Khokhlov-ZabolotskayaKuznetsov or Ostrovsky-Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting because of two reasons: (1) the equations admit exact analytic solutions and (2)