For the sake of intellectual curiosity, in this manuscript we analyse the soliton solutions of a dynamical model namely, the \((2 + 1)\) -dimensional generalised Bogoyavlensky–Konopelchenko equation arising in mathematical physics. We apply the Hirota bilinear method and the unified method to produce a variety of novel solutions. By using the aforementioned techniques, we establish fresh sorts of solutions for the concern problem, including breather wave, lump-periodic, two wave solutions, dark, periodic, and rational soliton solutions. In addition, we describe the stability analysis of our chosen model. For certain values of the required free parameters, the propagation of the derived well-furnished outcomes is visualised in different profiles using Mathematica 13.0. All of the findings in this study are crucial to comprehending the physical significance and behaviour of the investigated equation, which highlights the significance of examining various nonlinear wave phenomena in mathematical physics. The acquired results demonstrate that the computational strategies used are efficient, competent, and concise and may be used in conjunction with representative computations to apply to more complicated phenomena.
