Non-linear plane waves in materials having hexagonal internal structure

Three different continuum limits for modeling non-linear plane waves in two-dimensional hexagonal lattice are obtained. New coupled non-linear continuum equations are obtained to study the interaction of a macro-strain wave and the waves caused by variations in an internal structure. New analytical solutions are obtained to describe localized non-linear strain waves. It is shown that the solutions are different from those of the 1D lattice model due to the inclusion of non-neighboring interactions in a lattice.