Applications of nonlinear longitudinal wave equation with periodic optical solitons wave structure in magneto electro elastic circular rod

In this research work, we utilized the auxiliary equation technique and extracted the optical soliton solutions to the nonlinear longitudinal wave equation (NLLWE) in magneto electro elastic (MEE) rod that was spread out in a circle. The NLLWE in MEE systems deals with the mathematical physics of transverse Poisson’s effect dispersal and also very important in many engineering fields like sensors and actuators. As a result, we extracted the exact soliton solutions in bright solitons, dark solitons, kink wave solitons, anti-kink wave solitons, combined bright-dark solitons, solitary waves and periodic singular solitons. The physical structure of some extracted solutions visualizing in contour, two, and three dimensions through numerical simulation. The explored soliton solutions are interested, more general and having different physical structure, which may will be helpful to study of physical phenomena in the fields of optical fibers, plasma physics, soliton wave theory, nonlinear optics, ocean engineering, nonlinear dynamics and different branches of applied sciences. The successful extraction of exact solitons shows that this utilized approach is effective, straightforward, concise and powerful can also applicable to other nonlinear partial differential equations that involve in mathematical physics, engineering and applied sciences.