Abstract
In this study, several novel solutions of strain wave equation for micro-structured solids are obtained by using the powerful modified extended direct algebraic method. In microstructured solids, the strain wave dynamical equation is utilized to model the wave propagation in micro-structured materials. We have profitably obtained exact traveling wave solutions, including solitons, solitary waves, kink and anti-kink solitary waves, periodic and rational solutions have been found. This approach can not only produce the same solution, but also find new solutions that we think other researchers have missed. These attained solutions help researchers for knowing the physical phenomena of this dynamical equation. The three-dimensional maps of some solutions obtained in this study are plotted through giving appropriate values of the parameters engaged in the solutions for knowing the physical interpretation. The computational work and obtained results demonstrate that the new extended technique, gives an efficient and direct mathematical tools for resolving the nonlinear models in engineering and mathematical physics.