The present article deals with the symmetry reductions and invariant solutions of breaking soliton equation by virtue of similarity transformation method. The equation represents the collision of a Riemann wave propagating along the $y$-axis with a long wave along the $x$-axis. The infinitesimal transformations under one parameter for the governing system have been derived by exploiting the invariance property of Lie group theory. Consequently, the number of independent variables is reduced by one and the system remains invariant. A repeated application transforms the governing system into systems of ordinary differential equations. These systems degenerate well-known soliton solutions under some limiting conditions. The obtained solutions are extended with numerical simulation resulting in dark solitons, lumps, compactons, multisolitons, stationary and parabolic profiles and are shown graphically.