<p>In this paper, the state transition and branch structures of nonlinear waves in Kadomtsev–Petviashvili (KP)-based system are investigated, which plays an important role in plasma physics, fluid mechanics and gas dynamics. One-breath wave solutions, two- and three-lump chains are constructed by adding constraints to the soliton solutions. A series of converted nonlinear waves are generated by controlling the parameter ratio of the one-breath wave. The amplitude, oscillation law and time-varying dynamics of these waves are studied with the aid of characteristic lines analysis. The gradient relationship of these transformed nonlinear waves is demonstrated through a Riemannian circle. Analytical solutions for each branch before and after the interaction of the lump chains are obtained through asymptotic analysis. We define the resonant lump chain structures as branch structures. Two types of resonant branch structures are presented, which contain the Y-shaped branch structure and two V-shaped branch structures. The novelty of this paper lies in the fact that the breath wave solutions applied to the study of the transformation mechanism are based on Hirota’s bilinear method, which is relatively rare in the study of the transformation mechanism of Schrödinger-type equation. This study is helpful for us to investigate the transformation mechanism of the Schrödinger-type equation and the resonant interaction between the different kinds of nonlinear waves.</p>