Painlevé property, soliton-like solutions and complexitons for a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model

As a model derived from a two-layer fluid system which describes the atmospheric and oceanic phenomena, a coupled variable-coefficient modified Korteweg–de Vries system is concerned in this paper. With the help of symbolic computation, its integrability in the Painlevé sense is investigated. Furthermore, Hirota’s bilinear method is employed to construct the bilinear forms through the dependent variable transformations, and soliton-like solutions and complexitons are derived. Finally, effects of variable coefficients are discussed graphically, and it is concluded that the variable coefficients control the propagation trajectories of solitons and complexitons.