Wronskian and rational solutions of a $$(2+1)$$-dimensional nonlinear evolution equation with time-dependent coefficients

Abstract This study investigates an extended $$(2+1)$$ ( 2 + 1 ) -dimensional nonlinear evolution equation with time-dependent coefficients that describe nonlinear wave dynamics in variable environments. While previous studies predominantly considered cases of constant-coefficients, we investigate how temporal variability influences the formation and dynamics of nonlinear structures. By applying the Wronskian technique, we establish explicit Wronskian solutions and derive general N -soliton and resonant Y-type soliton configurations. Using a symbolic-computation-based bilinear approach combined with the variable transformation $$X=x-\omega {(t)}$$ X = x - ω ( t ) , we further construct higher-order rational solutions that capture both soliton and rogue-wave behavior. Introducing two free parameters $$\alpha $$ α and $$\beta $$ β , enables the generation of tunable rogue-wave patterns with controllable center locations. The results highlight new interaction phenomena and reveal the significant role played by time-dependent coefficients in shaping the evolution of solitons and rogue waves, offering insights applicable to fluid dynamics, optics, and plasma systems.