N-soliton, Hth-order breather, hybrid and multi-pole solutions for a generalized variable-coefficient Gardner equation with an external force in a plasma or fluid

In this paper, we investigate a generalized variable-coefficient Gardner equation with an external force in a plasma or fluid. Via the Hirota method, we obtain certain bilinear forms and N-soliton solutions, where N is a positive integer. We also derive the Hth-order breather and hybrid solutions through the complex conjugated transformations, where H is a positive integer. Moreover, multi-pole solutions are constructed with the limit method. Multi-soliton, breather-breather, soliton-breather and multi-pole interactions are studied. Influences of the external force and variable coefficients on the solutions are discussed analytically and graphically. For those nonlinear waves: (i) the external force affects the backgrounds and velocities; (ii) the damping coefficient affects the amplitudes, widths and velocities; (iii) the dispersive and dissipative coefficients affect the characteristic lines and velocities.