Abstract
In this paper, our aim is to construct the novel wave structures for two non-linear evolution equations which are rising in non-linear optics, mathematical biological models, fluid dynamics, waves theory, mechanics, quantum mechanics, and many more. We employed an efficient analytical technique namely, the Sardar-subequation method to build the wave solutions for the modified Benjamin-Bona-Mahony equation and the Coupled Klein–Gordon equations. We have built the numerous type of soliton wave structures of modified Benjamin-Bona-Mahony equation and the Coupled Klein–Gordon equations via the Sardar-subequation method. Acquired results reveal the dynamics behavior of waves structures including the bright, singular, dark, and periodic singular solitons solutions. To illustrate the behavior of these solutions some selected solutions are sketched in two-, and three-dimensional graphs. On the basis of these results, our technique is suitable, up-to-date, and powerful. The obtained solutions are very efficacious and influential in non-linear optics, mathematical biology, mechanics, fluid mechanics, plasma physics, and many more. This study will assist to predict some new hypothesis and theories in the field of mathematical physics.