Computer simulation of solitary waves in a common or auxetic elastic rod with both quadratic and cubic nonlinearities

Abstract

Abstract Results of numerical simulations are presented for propagation of solitary waves in an elastic rod of positive or negative Poisson's ratio, i.e. of a common or auxetic material. Splitting of various initial pulses during propagation into a sequence of solitary waves is considered in frames of a model which contains both quadratic and cubic nonlinear terms. The obtained results are compared with some exact analytic solutions, called solitons, what leads to the conclusion that the solitons describe well the more complicated wave fields which are obtained by numerical simulations. This is because the analytic solutions reflect complete balance between various orders of nonlinearity and dispersion. Collisions between some obtained solitary waves are also presented.