Wronskian solutions and integrability for a generalized variable-coefficient forced Korteweg-de Vries equation in fluids

Under investigation in this paper is a generalized variable-coefficient forced Korteweg-de Vries equation, which can describe the shallow-water waves, internal gravity waves, and so on. With symbolic computation, the soliton solutions in the Wronskian form are derived based on the given bilinear form. Bäcklund transformation and Lax pair for such equation are also constructed. Variable coefficients and parameters of three solitons are managed to observe the features of the solitonic propagation and interaction, e.g.; the solitonic velocity, amplitude and background. Our results could be expected to benefit the relevant problems in fluids.