Resonant lump chain interactions of a (2+1)-dimensional generalized Korteweg–de Vries equation in plasma physics and fluid dynamics

In this paper, we mainly study the resonant interactions of lump chains of (2+1)-dimensional generalized Korteweg–de Vries (gKdV) equation, which can be used to describe the nonlinear wave phenomena in plasma physics, weakly dispersive media and fluid dynamics. We construct the lump chain solutions by adding some constraints to the soliton solutions of the gKdV equation. Then through the asymptotic analysis, the analytical solution of each branch of the lump chains after interaction is obtained. Through the phase shift analysis of the analytical solution, we get the condition of resonance, and then the resonant interactions of the two- and three-lump chains are analyzed in detail. In particular, we explore two cases including the cross-resonant interaction and parallel-resonant interaction of the lump chains. In addition, 2D and 3D images are used to describe the spatial evolution of resonant interactions. The results can further help us study the resonant interactions between the lump chains and other nonlinear waves.