Stability, modulation instability analysis and new travelling wave solutions of non-dissipative double-dispersive microstrain wave model within micro-structured solids

This manuscript offers an in-depth analysis of the behavior of non-dissipative double-dispersive microstrain waves within microstructured solids, employing the Sardar sub-equation (SSE) technique. The presentation unfolds as follows: Firstly, we introduce the general algorithm underpinning the SSE technique. Subsequently, we apply the traveling wave transform to the given equation, thereby transforming it into a nonlinear ordinary differential (NLOD) equation. Using this novel approach, we derive a series of remarkable soliton solutions for the aforementioned model. The stability and modulation instability analysis are also presented. The obtained solutions encompass singular solitons, bright solitons, multi M-shaped solitons, as well as the interaction of singular solitons with periodic solitons and bright periodic solitons. Furthermore, we numerically simulate the exact analytical soliton solutions and meticulously investigate the influence of various parameters on the characteristics of these soliton waves.