Painleve analysis, auto-Backlund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation

There has been considerable interest in the study on the variable-coefficient nonlinear evolution equations in recent years, since they can describe the real situations in many fields of physical and engineering sciences. In this paper, a generalized variable-coefficient KdV (GvcKdV) equation with the external-force and perturbed/dissipative terms is investigated, which can describe the various real situations, including large-amplitude internal waves, blood vessels, Bose-Einstein condensates, rods and positons. The Painleve analysis leads to the explicit constraint on the variable coefficients for such a equation to pass the Painleve test. An auto-Backlund transformation is provided by use of the truncated Painleve expansion and symbolic computation. Via the given auto-Backlund transformation, three families of analytic solutions are obtained, including the solitonic and periodic solutions.