An asymptotic procedure is developed to obtain governing two-dimensional nonlinear equations as a result of the continuum limits of the original discrete hexagonal lattice model. Possible continualization is analyzed on the basis of linearized discrete equations. New weakly nonlinear continuum equations for plane and weakly transverse disturbed shear waves in a hexagonal lattice are obtained using different continuum limits. It is shown that nonlinear plane shear waves are described different from the model of isotropic continuum.
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