<p>In this work, we study wave state transitions of the (2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani (2KdVSKR) equation by analyzing the characteristic line and phase shift. By converting the wave parameters of the N-soliton solution into complex numbers, the breath wave solution is constructed. The lump wave solution is derived through the long wave limit method. Then, by choosing appropriate parameter values, we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters. Furthermore, we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components. Subsequently, locality, oscillation properties and evolutionary phenomenon of the transformed waves are presented. And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution. Finally, for higher-order waves, a range of interaction models are depicted along with their evolutionary phenomena. And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.</p>