Abstract
The aim of the present study is to identify multiple soliton solutions to the nonlinear coupled Broer-Kaup-Kupershmidt (BKK) system, including beta, conformable, local-fractional, and M-truncated derivatives. The coupled Broer-Kaup-Kupershmidt system is employed for modelling nonlinear wave evolution in mathematical models of fluid dynamics, plasmic, optical, dispersive, and nonlinear long-gravity waves. The travelling wave solutions to the above model are found using the Unified and generalised Bernoulli sub-ODE techniques. By modifying certain parameter values, we may create bright soliton, squeezed bell-shaped wave, expanded v-shaped soliton, W-shaped wave, singular soliton, and periodic solutions. The four distinct kinds of derivatives are compared quite effectively using 2D line graphs. Also, contour plots and 3D graphics are given by using Mathematica 10. Lastly, any pair of propagating wave solutions has symmetrical geometrical forms.