In the present research, similarity transformation method via Lie-group theory is proposed to seek some more exact closed form solutions of the (2+1)-dimensional breaking soliton system. The system describes the interactions of the Riemann wave along y-axis and long wave along x-axis. Some explicit solutions of breaking soliton system are attained with appropriate choices of the arbitrary functions and making use of arbitrary constants involved in the infinitesimals. In order to obtain physically meaningful solutions, numerical simulation is performed. On the basis of graphical representation, the physical analysis of solutions reveals into multi-solitons, periodic, quadratic, asymptotic and stationary profiles.