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This study considers a totally new (2+1)-D KdV model to investigate multi-soliton solutions and their dynamical collisions. We derive its multi-soliton solutions, and then taking complex values of the involved free parameters, we generate various interaction solutions in the form of multi-rogue, periodic rogue, double complexiton, and triple complexiton waves, and discuss their collisions. The nonlinearity effects that arise in nonlinear dynamics of phonon packets in crystals, shallow water, plasma as well as ion acoustic waves can be visualized through the derived interaction solutions. All the solutions are depicted by 3d-plots and contour plots.