Abstract
In this work, we study the generalized variable-coefficient Gardner equation (GVG) with nonlinear terms of any order and forcing term, abundant new exact solutions for the equation are obtained by using the general mapping deformation method with the aid of symbolic computation, which include several kinds of types such as Jacobi elliptic wave-like solutions, soliton-like solutions, trigonometric function solutions, Weierstrass elliptic function solution and rational type solution. Some of them are found for the first time, which shows that the applied method is more powerful and will be used in further works to establish more entirely new exact solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.
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