Dispersive optical solitary wave solutions of strain wave equation in micro-structured solids and its applications

Abstract

The new technique of modified extended mapping technique is an important, prevailing and direct Mathematical tool for constructing exact solutions in the form of traveling waves of non-linear evolution equations (NLEEs) in applied science and engineering. The dispersive effect of the combination of the microstructure and nonlinearity of the material can produce solitary waves. In micro-structured solids, the wave propagation in microstructured materials is modeled by strain wave mechanics equation. In this paper, several new solutions of strain wave dynamical model for micro-structured solids are obtained by using the strongly modified extended mapping technique. We obtain exact waves solutions, including solitons, solitary waves, kinks and anti-kink solitary waves, periodic and rational solutions which have key applications and useful for researchers to understand the phenomena. The three-dimensional graphs and contour plots of some solutions attained in this study are drawn by giving the suitable values of the parameters used to understand the solutions of physical interpretation. The model stability is studied via modulational instability analysis and dispersion relation is derived which verify that these solutions are stable. The computational work and the results demonstrate that the new extended technique is effective and influential.