Dynamics Investigation and Solitons Formation for $$(2+1)$$ -Dimensional Zoomeron Equation and Foam Drainage Equation

Abstract The prime goal of this study is to investigate novel solutions two well-known nonlinear models namely the $$(2+1)$$ ( 2 + 1 ) -dimensional Zoomeron equation and foam drainage by utilizing a powerful technique; extended $$\left(\frac{G'}{G^{2}}\right)$$ G ′ -expansion method. Using methodology, hyperbolic function solutions, trigonometric rational are constructed. Abundant soliton retrieved from obtained results. dynamical structures illustrated graphically through 3-dimensional graphs corresponding contour plots. reported results depict effectiveness capability method for handling different partial differential equations.