We qualitatively analyze the bounded traveling wave solutions of a (2+1)- dimensional generalized breaking soliton (gBS) equation by using the theory of planar dynamical systems. We present the global phase diagrams of the dynamical system corresponding to the (2+1)-dimensional gBS equation under different parameters. The conditions for the existence of bounded traveling wave solutions are successfully derived. We find the relationship between the waveform of bounded traveling wave solutions and the dissipation coefficient $β.$ When the absolute value of the dissipation coefficient $β$ is greater than a critical value, we find that the equation has a kink profile solitary wave solution, while the solution has oscillatory and damped property if $|β|$ is less than the critical value. In addition, we give the exact bell profile solitary wave solution and kink profile solitary wave solution by using undetermined coefficient method. The approximate oscillatory damped solution is given constructively. Through error analysis, we find that the approximate oscillatory damped solution is meaningful. Finally, we present the graphical analysis of the influence of dissipation coefficient $β$ on oscillatory damped solution in order to better understand their dynamical behaviors.