Generalized (2+1)-dimensional Gardner model: bilinear equations, Bäcklund transformation, Lax representation and interaction mechanisms

In the present paper, with symbolic computation, a generalized (2+1)-dimensional Gardner model with t dependence is directly studied without any reductions into constant-coefficient form. Integrable properties are investigated, which mainly include the bilinear equations, bilinear Bäcklund transformation, Lax representation and analytic solutions. Dynamic properties and interaction mechanisms (inelastic compression/amplification interactions) for the shock waves are also revealed by means of the asymptotic analysis and graphical simulations.