This work aims to present nonlinear models that arise in ocean engineering. There are many models of ocean waves that are present in nature. In shallow water, the linearization of the equations requires critical conditions on wave capacity than it make in deep water, and the strong nonlinear belongings are spotted. We use Lie symmetry analysis to obtain different types of soliton solutions like one, two, and three-soliton solutions in a (2+1) dimensional variable-coefficient Bogoyavlensky Konopelchenko (VCBK) equation that describes the interaction of a Riemann wave reproducing along the y-axis and a long wave reproducing along the x-axis in engineering and science. We use the Lie symmetry analysis then the integrating factor method to obtain new solutions of the VCBK equation. To demonstrate the physical meaning of the solutions obtained by the presented techniques, the graphical performance has been demonstrated with some values. The presented equation has fewer dimensions and is reduced to ordinary differential equations using the Lie symmetry technique.