N-soliton solutions, Backlund transformation and Lax Pair for a generalized variable-coefficient cylindrical Kadomtsev-Petviashvili equation

In this paper, we investigate a generalized variable-coefficient cylindrical Kadomtsev-Petviashvili equation, which characterizes the water waves propagation in the fluid dynamics. Via the generalized Laurent series truncated at the constant-level term, an auto-Backlund transformation is derived. We establish the bilinear form through the utilization of the Bell polynomials. Based on the Hirota method, we construct the N-soliton solutions. We derive the bilinear Backlund transformation and Lax pair by virtue of the Hirota bilinear operators' exchange formulae and symbolic computation.