Optical solitons of SMCH model in mathematical physics: impact of wind and friction on wave

The simplified modified Camassa–Holm (SMCH) model is widely recognized in the fields of plasma physics, bio-mathematics, and optical fibers. In this study, we have explored the SMCH model implementing the improved Bernoulli sub-equation function (IBSEF) method to obtain novel traveling wave solitons. Our investigation has yielded broad-ranging analytical solutions for the SMCH equation, including hyperbolic, trigonometric, and exponential solutions. Furthermore, we have analyzed the impact of wind and friction on water waves by employing the free parameters of the obtained solutions which can play a crucial role in nature. These findings hold significant relevance to the study of natural phenomena. Moreover, we have discussed the parametric effects of the obtained solitons on the wave profile of the system, revealing kink, bright, and dark-type solitons. Our findings suggest that the IBSEF method is reliable and can be used in future studies to determine different and novel soliton explanations of various nonlinear evolution equations encountered in mathematical physics and engineering.