Madadi, MajidAkinyemi, LanreHosseini, Kamyar2026-03-152026-03-1520260924-090X1573-269X10.1007/s11071-025-12151-72-s2.0-105031086254https://doi.org/10.1007/s11071-025-12151-7https://hdl.handle.net/20.500.14517/8918This study investigates an extended (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), we further construct higher-order rational solutions that capture both soliton and rogue-wave behavior. Introducing two free parameters alpha and beta, 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.eninfo:eu-repo/semantics/openAccessNonlinear Wave PropagationWronskian MethodSolitonRational SolutionsLump and Rogue-Wave StructuresArticle