文摘
In this paper, the Riemann–Bäcklund method is extended to a generalized variable coefficient (\(2+1\))-dimensional Korteweg–de Vries equation. The soliton and quasiperiodic wave solutions are investigated systematically. The relations between the quasiperiodic wave solutions and the soliton solutions are rigorously established by a limiting procedure. It is proved that the periodic wave solutions tend to the soliton solutions under a small amplitude limit. Furthermore, the propagation characteristics of the soliton solutions and periodic wave solutions are discussed through the graphical analysis.