Analytic N-solitary-wave solution of a variable-coefficient Gardner equation from fluid dynamics and plasma physics

In this paper, the investigation is focused on a variable-coefficient Gardner equation with quadric and cubic nonlinearities from fluid dynamics and plasma physics. Using the Hirota bilinear method, the one-, two- and three-solitary-wave solutions of the variable-coefficient Gardner equation are derived, and the analytic N-solitary-wave solution is presented for the first time in this paper with the aid of symbolic computation. Figures are plotted to illustrate the solutions obtained in this paper.