Nonautonomous characteristics of lump solutions for a (2+1)-dimensional Korteweg–de Vries equation with variable coefficients

We study a (2+1)-dimensional Korteweg–de Vries (KdV) equation with variable coefficients. By virtue of Hirota method, we present three types of nonautonomous lump solutions including the bright, bright–dark and dark lump ones. By considering different types of dispersion coefficients, we investigate the characteristics of trajectories, velocities and displacements of nonautonomous bright lump wave, which are different from the case of its constant-coefficient counterpart. We finally demonstrate the periodic attraction and repulsion interaction between a lump wave and a soliton. Our results might provide some physical insights into the relevant fields in nonlinear science.