Improved description of longitudinal strain solitary waves

It is found that simultaneous existence of compressive and tensile localized strain solitary waves in a rod can be described by the model equation containing both quadratic and cubic nonlinear terms. Only propagation of these waves is described by exact travelling wave solutions. However, numerical solution demonstrates that both kinds of these waves may be generated from an arbitrary input and interact each other keeping their shape and velocity. Moreover, one and the same input gives rise to a different number of these kinds of waves, and it is quadratic nonlinearity that determines it.